## How to Solve Quadratic Equations using the Square Root Method

This is the “best” method whenever the quadratic equation only contains {x^2} terms. That implies no presence of any x term being raised to the first power somewhere in the equation.

## Key Strategy in Solving Quadratic Equations using the Square Root Method

## Examples of How to Solve Quadratic Equations by Square Root Method

Example 1 : Solve the quadratic equation below using the Square Root Method.

Example 2 : Solve the quadratic equation below using the Square Root Method.

The final answers are x = 4 and x = - \,4 .

Example 3 : Solve the quadratic equation below using the Square Root Method.

The solutions to this quadratic formula are x = 3 and x = - \,3 .

Example 4 : Solve the quadratic equation below using the Square Root Method.

Example 5 : Solve the quadratic equation below using the Square Root Method.

There’s an x -squared term left after the first application of square root.

Now we have to break up {x^2} = \pm \,6 + 10 into two cases because of the “plus” or “minus” in 6 .

Example 6 : Solve the quadratic equation below using the Square Root Method.

Example 7 : Solve the quadratic equation below using the Square Root Method.

You might also be interested in:

To log in and use all the features of Khan Academy, please enable JavaScript in your browser.

## Unit 10: Lesson 2

- Intro to square-root equations & extraneous solutions
- Square-root equations intro
- Intro to solving square-root equations
- Solving square-root equations
- Solving square-root equations: one solution
- Solving square-root equations: two solutions
- Solving square-root equations: no solution

## Square Roots Calculator

Find square roots of any number step-by-step.

- Prime Factorization
- Add, Subtract
- Mixed Numbers
- Improper Fractions
- Long Addition
- Long Subtraction
- Long Multiplication
- Long Division
- Add/Subtract
- Multiplication
- Decimal to Fraction
- Fraction to Decimal
- Rounding New
- Square Roots
- Ratios & Proportions
- Arithmetic Mean
- Scientific Notation Arithmetics New

## Most Used Actions

## Related Symbolab blog posts

Message received. Thanks for the feedback.

## Generating PDF...

- school Campus Bookshelves
- menu_book Bookshelves
- perm_media Learning Objects
- login Login
- how_to_reg Request Instructor Account
- hub Instructor Commons
- Download Page (PDF)
- Download Full Book (PDF)
- Periodic Table
- Physics Constants
- Scientific Calculator
- Reference & Cite
- Tools expand_more
- Readability

selected template will load here

## 9.2: Solve Quadratic Equations Using the Square Root Property

## Learning Objectives

By the end of this section, you will be able to:

- Solve quadratic equations of the form \(ax^{2}=k\) using the Square Root Property
- Solve quadratic equations of the form \(a(x–h)^{2}=k\) using the Square Root Property

Before you get started, take this readiness quiz.

- Simplify: \(\sqrt{128}\). If you missed this problem, review Example 8.13.
- Simplify: \(\sqrt{\frac{32}{5}}\). If you missed this problem, review Example 8.50.
- Factor: \(9 x^{2}-12 x+4\). If you missed this problem, review Example 6.23.

## Solve Quadratic Equations of the Form \(ax^{2}=k\) using the Square Root Property

Put the equation in standard form.

Factor the difference of squares.

Use the Zero Produce Property.

If \(n^{2}=m\), then \(n\) is a square root of \(m\).

## Definition \(\PageIndex{1}\)

\(x=\sqrt{k} \quad\) or \(\quad x=-\sqrt{k} \quad\) or \(\quad x=\pm \sqrt{k}\)

Now we will solve the equation \(x^{2}=9\) again, this time using the Square Root Property.

Use the Square Root Property. \(x=\sqrt{7}, \quad x=-\sqrt{7}\)

We cannot simplify \(\sqrt{7}\), so we leave the answer as a radical.

## Example \(\PageIndex{1}\) How to Solve a Quadratic Equation of the form \(ax^{2}-k\) Using the Square Root Property

## Exercise \(\PageIndex{1}\)

\(x=4 \sqrt{3}, x=-4 \sqrt{3}\)

## Exercise \(\PageIndex{2}\)

\(y=3 \sqrt{3}, y=-3 \sqrt{3}\)

The steps to take to use the Square Root Property to solve a quadratic equation are listed here.

## Solve a Quadratic Equation Using the Square Root Property

- Isolate the quadratic term and make its coefficient one.
- Use Square Root Property.
- Simplify the radical.
- Check the solutions.

## Example \(\PageIndex{2}\)

## Exercise \(\PageIndex{3}\)

## Exercise \(\PageIndex{4}\)

## Example \(\PageIndex{3}\)

## Exercise \(\PageIndex{5}\)

\(c=2 \sqrt{3} i, \quad c=-2 \sqrt{3} i\)

## Exercise \(\PageIndex{6}\)

\(c=2 \sqrt{6} i, \quad c=-2 \sqrt{6} i\)

## Example \(\PageIndex{4}\)

Solve: \(\frac{2}{3} u^{2}+5=17\).

## Exercise \(\PageIndex{7}\)

Solve: \(\frac{1}{2} x^{2}+4=24\).

\(x=2 \sqrt{10}, x=-2 \sqrt{10}\)

## Exercise \(\PageIndex{8}\)

Solve: \(\frac{3}{4} y^{2}-3=18\).

\(y=2 \sqrt{7}, y=-2 \sqrt{7}\)

## Example \(\PageIndex{5}\)

## Exercise \(\PageIndex{9}\)

\(r=\frac{6 \sqrt{5}}{5}, \quad r=-\frac{6 \sqrt{5}}{5}\)

## Exercise \(\PageIndex{10}\)

\(t=\frac{8 \sqrt{3}}{3}, \quad t=-\frac{8 \sqrt{3}}{3}\)

## Solve Quadratic Equation of the Form \(a(x-h)^{2}=k\) Using the Square Root Property

## Example \(\PageIndex{6}\)

## Exercise \(\PageIndex{11}\)

\(a=3+3 \sqrt{2}, \quad a=3-3 \sqrt{2}\)

## Exercise \(\PageIndex{12}\)

\(b=-2+2 \sqrt{10}, \quad b=-2-2 \sqrt{10}\)

## Example \(\PageIndex{7}\)

Solve: \(\left(x-\frac{1}{3}\right)^{2}=\frac{5}{9}\).

\(\left(x-\frac{1}{3}\right)^{2}=\frac{5}{9}\)

\(x-\frac{1}{3}=\pm \sqrt{\frac{5}{9}}\)

Rewrite the radical as a fraction of square roots.

\(x-\frac{1}{3}=\pm \frac{\sqrt{5}}{\sqrt{9}}\)

\(x-\frac{1}{3}=\pm \frac{\sqrt{5}}{3}\)

\(x=\frac{1}{3} \pm \frac{\sqrt{5}}{3}\)

Rewrite to show two solutions.

\(x=\frac{1}{3}+\frac{\sqrt{5}}{3}, x=\frac{1}{3}-\frac{\sqrt{5}}{3}\)

## Exercise \(\PageIndex{13}\)

Solve: \(\left(x-\frac{1}{2}\right)^{2}=\frac{5}{4}\).

\(x=\frac{1}{2}+\frac{\sqrt{5}}{2}, x=\frac{1}{2}-\frac{\sqrt{5}}{2}\)

## Exercise \(\PageIndex{14}\)

Solve: \(\left(y+\frac{3}{4}\right)^{2}=\frac{7}{16}\).

\(y=-\frac{3}{4}+\frac{\sqrt{7}}{4}, y=-\frac{3}{4}-\frac{\sqrt{7}}{4}\)

We will start the solution to the next example by isolating the binomial term.

## Example \(\PageIndex{8}\)

Subtract \(3\) from both sides to isolate the binomial term.

\(x=2+3 \sqrt{3}, x=2-3 \sqrt{3}\)

## Exercise \(\PageIndex{15}\)

\(a=5+2 \sqrt{5}, a=5-2 \sqrt{5}\)

## Exercise \(\PageIndex{16}\)

\(b=-3+4 \sqrt{2}, \quad b=-3-4 \sqrt{2}\)

Sometimes the solutions are complex numbers.

## Example \(\PageIndex{9}\)

\(x=\frac{3 \pm 2 \sqrt{3 i}}{2}\)

\(x=\frac{3}{2} \pm \frac{2 \sqrt{3} i}{2}\)

\(x=\frac{3}{2} \pm \sqrt{3} i\)

\(x=\frac{3}{2}+\sqrt{3} i, x=\frac{3}{2}-\sqrt{3} i\)

## Exercise \(\PageIndex{17}\)

\(r=-\frac{4}{3}+\frac{2 \sqrt{2} i}{3}, r=-\frac{4}{3}-\frac{2 \sqrt{2} i}{3}\)

## Exercise \(\PageIndex{18}\)

\(t=4+\frac{\sqrt{10} i}{2}, t=4-\frac{\sqrt{10 i}}{2}\)

## Example \(\PageIndex{10}\)

We notice the left side of the equation is a perfect square trinomial. We will factor it first.

## Exercise \(\PageIndex{19}\)

## Exercise \(\PageIndex{20}\)

Solve: \(16 n^{2}+40 n+25=4\).

\(n=-\frac{3}{4}, \quad n=-\frac{7}{4}\)

- Solving Quadratic Equations: The Square Root Property
- Using the Square Root Property to Solve Quadratic Equations

## Key Concepts

- 9.1 Solve Quadratic Equations Using the Square Root Property
- Introduction
- 1.1 Use the Language of Algebra
- 1.2 Integers
- 1.3 Fractions
- 1.4 Decimals
- 1.5 Properties of Real Numbers
- Key Concepts
- Review Exercises
- Practice Test
- 2.1 Use a General Strategy to Solve Linear Equations
- 2.2 Use a Problem Solving Strategy
- 2.3 Solve a Formula for a Specific Variable
- 2.4 Solve Mixture and Uniform Motion Applications
- 2.5 Solve Linear Inequalities
- 2.6 Solve Compound Inequalities
- 2.7 Solve Absolute Value Inequalities
- 3.1 Graph Linear Equations in Two Variables
- 3.2 Slope of a Line
- 3.3 Find the Equation of a Line
- 3.4 Graph Linear Inequalities in Two Variables
- 3.5 Relations and Functions
- 3.6 Graphs of Functions
- 4.1 Solve Systems of Linear Equations with Two Variables
- 4.2 Solve Applications with Systems of Equations
- 4.3 Solve Mixture Applications with Systems of Equations
- 4.4 Solve Systems of Equations with Three Variables
- 4.5 Solve Systems of Equations Using Matrices
- 4.6 Solve Systems of Equations Using Determinants
- 4.7 Graphing Systems of Linear Inequalities
- 5.1 Add and Subtract Polynomials
- 5.2 Properties of Exponents and Scientific Notation
- 5.3 Multiply Polynomials
- 5.4 Dividing Polynomials
- Introduction to Factoring
- 6.1 Greatest Common Factor and Factor by Grouping
- 6.2 Factor Trinomials
- 6.3 Factor Special Products
- 6.4 General Strategy for Factoring Polynomials
- 6.5 Polynomial Equations
- 7.1 Multiply and Divide Rational Expressions
- 7.2 Add and Subtract Rational Expressions
- 7.3 Simplify Complex Rational Expressions
- 7.4 Solve Rational Equations
- 7.5 Solve Applications with Rational Equations
- 7.6 Solve Rational Inequalities
- 8.1 Simplify Expressions with Roots
- 8.2 Simplify Radical Expressions
- 8.3 Simplify Rational Exponents
- 8.4 Add, Subtract, and Multiply Radical Expressions
- 8.5 Divide Radical Expressions
- 8.6 Solve Radical Equations
- 8.7 Use Radicals in Functions
- 8.8 Use the Complex Number System
- 9.2 Solve Quadratic Equations by Completing the Square
- 9.3 Solve Quadratic Equations Using the Quadratic Formula
- 9.4 Solve Equations in Quadratic Form
- 9.5 Solve Applications of Quadratic Equations
- 9.6 Graph Quadratic Functions Using Properties
- 9.7 Graph Quadratic Functions Using Transformations
- 9.8 Solve Quadratic Inequalities
- 10.1 Finding Composite and Inverse Functions
- 10.2 Evaluate and Graph Exponential Functions
- 10.3 Evaluate and Graph Logarithmic Functions
- 10.4 Use the Properties of Logarithms
- 10.5 Solve Exponential and Logarithmic Equations
- 11.1 Distance and Midpoint Formulas; Circles
- 11.2 Parabolas
- 11.3 Ellipses
- 11.4 Hyperbolas
- 11.5 Solve Systems of Nonlinear Equations
- 12.1 Sequences
- 12.2 Arithmetic Sequences
- 12.3 Geometric Sequences and Series
- 12.4 Binomial Theorem

## Learning Objectives

By the end of this section, you will be able to:

- Solve quadratic equations of the form a x 2 = k a x 2 = k using the Square Root Property
- Solve quadratic equations of the form a ( x – h ) 2 = k a ( x – h ) 2 = k using the Square Root Property

## Be Prepared 9.1

Before you get started, take this readiness quiz.

Simplify: 128 . 128 . If you missed this problem, review Example 8.13 .

## Be Prepared 9.2

Simplify: 32 5 32 5 . If you missed this problem, review Example 8.50 .

## Be Prepared 9.3

Factor: 9 x 2 − 12 x + 4 9 x 2 − 12 x + 4 . If you missed this problem, review Example 6.23 .

## Solve Quadratic Equations of the form a x 2 = k a x 2 = k using the Square Root Property

## Square Root Property

Now we will solve the equation x 2 = 9 again, this time using the Square Root Property.

We cannot simplify 7 7 , so we leave the answer as a radical.

## Example 9.1

How to solve a quadratic equation of the form ax 2 = k using the square root property.

Solve: x 2 − 50 = 0 . x 2 − 50 = 0 .

Solve: x 2 − 48 = 0 . x 2 − 48 = 0 .

Solve: y 2 − 27 = 0 . y 2 − 27 = 0 .

The steps to take to use the Square Root Property to solve a quadratic equation are listed here.

## Solve a quadratic equation using the square root property.

- Step 1. Isolate the quadratic term and make its coefficient one.
- Step 2. Use Square Root Property.
- Step 3. Simplify the radical.
- Step 4. Check the solutions.

## Example 9.2

Solve: 3 z 2 = 108 . 3 z 2 = 108 .

Solve: 2 x 2 = 98 . 2 x 2 = 98 .

Solve: 5 m 2 = 80 . 5 m 2 = 80 .

## Example 9.3

Solve: x 2 + 72 = 0 x 2 + 72 = 0 .

Solve: c 2 + 12 = 0 . c 2 + 12 = 0 .

Solve: q 2 + 24 = 0 . q 2 + 24 = 0 .

## Example 9.4

Solve: 2 3 u 2 + 5 = 17 . 2 3 u 2 + 5 = 17 .

Solve: 1 2 x 2 + 4 = 24 . 1 2 x 2 + 4 = 24 .

Solve: 3 4 y 2 − 3 = 18 . 3 4 y 2 − 3 = 18 .

## Example 9.5

Solve: 2 x 2 − 8 = 41 . 2 x 2 − 8 = 41 .

Solve: 5 r 2 − 2 = 34 . 5 r 2 − 2 = 34 .

## Try It 9.10

Solve: 3 t 2 + 6 = 70 . 3 t 2 + 6 = 70 .

Solve Quadratic Equations of the Form a ( x − h ) 2 = k Using the Square Root Property

## Example 9.6

Solve: 4 ( y − 7 ) 2 = 48 . 4 ( y − 7 ) 2 = 48 .

## Try It 9.11

Solve: 3 ( a − 3 ) 2 = 54 . 3 ( a − 3 ) 2 = 54 .

## Try It 9.12

Solve: 2 ( b + 2 ) 2 = 80 . 2 ( b + 2 ) 2 = 80 .

## Example 9.7

Solve: ( x − 1 3 ) 2 = 5 9 . ( x − 1 3 ) 2 = 5 9 .

## Try It 9.13

Solve: ( x − 1 2 ) 2 = 5 4 . ( x − 1 2 ) 2 = 5 4 .

## Try It 9.14

Solve: ( y + 3 4 ) 2 = 7 16 . ( y + 3 4 ) 2 = 7 16 .

We will start the solution to the next example by isolating the binomial term.

## Example 9.8

Solve: 2 ( x − 2 ) 2 + 3 = 57 . 2 ( x − 2 ) 2 + 3 = 57 .

## Try It 9.15

Solve: 5 ( a − 5 ) 2 + 4 = 104 . 5 ( a − 5 ) 2 + 4 = 104 .

## Try It 9.16

Solve: 3 ( b + 3 ) 2 − 8 = 88 . 3 ( b + 3 ) 2 − 8 = 88 .

Sometimes the solutions are complex numbers.

## Example 9.9

Solve: ( 2 x − 3 ) 2 = −12 . ( 2 x − 3 ) 2 = −12 .

## Try It 9.17

Solve: ( 3 r + 4 ) 2 = −8 . ( 3 r + 4 ) 2 = −8 .

## Try It 9.18

Solve: ( 2 t − 8 ) 2 = −10 . ( 2 t − 8 ) 2 = −10 .

## Example 9.10

Solve: 4 n 2 + 4 n + 1 = 16 . 4 n 2 + 4 n + 1 = 16 .

We notice the left side of the equation is a perfect square trinomial. We will factor it first.

## Try It 9.19

Solve: 9 m 2 − 12 m + 4 = 25 . 9 m 2 − 12 m + 4 = 25 .

## Try It 9.20

Solve: 16 n 2 + 40 n + 25 = 4 . 16 n 2 + 40 n + 25 = 4 .

- Solving Quadratic Equations: The Square Root Property
- Using the Square Root Property to Solve Quadratic Equations

## Section 9.1 Exercises

Solve Quadratic Equations of the Form ax 2 = k Using the Square Root Property

In the following exercises, solve each equation.

4 3 x 2 + 2 = 110 4 3 x 2 + 2 = 110

2 3 y 2 − 8 = −2 2 3 y 2 − 8 = −2

2 5 a 2 + 3 = 11 2 5 a 2 + 3 = 11

3 2 b 2 − 7 = 41 3 2 b 2 − 7 = 41

7 p 2 + 10 = 26 7 p 2 + 10 = 26

( u − 6 ) 2 = 64 ( u − 6 ) 2 = 64

( v + 10 ) 2 = 121 ( v + 10 ) 2 = 121

( m − 6 ) 2 = 20 ( m − 6 ) 2 = 20

( n + 5 ) 2 = 32 ( n + 5 ) 2 = 32

( r − 1 2 ) 2 = 3 4 ( r − 1 2 ) 2 = 3 4

( x + 1 5 ) 2 = 7 25 ( x + 1 5 ) 2 = 7 25

( y + 2 3 ) 2 = 8 81 ( y + 2 3 ) 2 = 8 81

( t − 5 6 ) 2 = 11 25 ( t − 5 6 ) 2 = 11 25

( a − 7 ) 2 + 5 = 55 ( a − 7 ) 2 + 5 = 55

( b − 1 ) 2 − 9 = 39 ( b − 1 ) 2 − 9 = 39

4 ( x + 3 ) 2 − 5 = 27 4 ( x + 3 ) 2 − 5 = 27

5 ( x + 3 ) 2 − 7 = 68 5 ( x + 3 ) 2 − 7 = 68

( 5 c + 1 ) 2 = −27 ( 5 c + 1 ) 2 = −27

( 8 d − 6 ) 2 = −24 ( 8 d − 6 ) 2 = −24

( 4 x − 3 ) 2 + 11 = −17 ( 4 x − 3 ) 2 + 11 = −17

( 2 y + 1 ) 2 − 5 = −23 ( 2 y + 1 ) 2 − 5 = −23

m 2 − 4 m + 4 = 8 m 2 − 4 m + 4 = 8

n 2 + 8 n + 16 = 27 n 2 + 8 n + 16 = 27

x 2 − 6 x + 9 = 12 x 2 − 6 x + 9 = 12

y 2 + 12 y + 36 = 32 y 2 + 12 y + 36 = 32

25 x 2 − 30 x + 9 = 36 25 x 2 − 30 x + 9 = 36

9 y 2 + 12 y + 4 = 9 9 y 2 + 12 y + 4 = 9

36 x 2 − 24 x + 4 = 81 36 x 2 − 24 x + 4 = 81

64 x 2 + 144 x + 81 = 25 64 x 2 + 144 x + 81 = 25

## Mixed Practice

In the following exercises, solve using the Square Root Property.

( a − 4 ) 2 = 28 ( a − 4 ) 2 = 28

( b + 7 ) 2 = 8 ( b + 7 ) 2 = 8

9 w 2 − 24 w + 16 = 1 9 w 2 − 24 w + 16 = 1

4 z 2 + 4 z + 1 = 49 4 z 2 + 4 z + 1 = 49

( p − 1 3 ) 2 = 7 9 ( p − 1 3 ) 2 = 7 9

( q − 3 5 ) 2 = 3 4 ( q − 3 5 ) 2 = 3 4

u 2 − 14 u + 49 = 72 u 2 − 14 u + 49 = 72

v 2 + 18 v + 81 = 50 v 2 + 18 v + 81 = 50

( m − 4 ) 2 + 3 = 15 ( m − 4 ) 2 + 3 = 15

( n − 7 ) 2 − 8 = 64 ( n − 7 ) 2 − 8 = 64

( x + 5 ) 2 = 4 ( x + 5 ) 2 = 4

( y − 4 ) 2 = 64 ( y − 4 ) 2 = 64

( x − 6 ) 2 + 7 = 3 ( x − 6 ) 2 + 7 = 3

( y − 4 ) 2 + 10 = 9 ( y − 4 ) 2 + 10 = 9

## Writing Exercises

In your own words, explain the Square Root Property.

ⓑ If most of your checks were:

As an Amazon Associate we earn from qualifying purchases.

Access for free at https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction

- Authors: Lynn Marecek, Andrea Honeycutt Mathis
- Publisher/website: OpenStax
- Book title: Intermediate Algebra 2e
- Publication date: May 6, 2020
- Location: Houston, Texas
- Book URL: https://openstax.org/books/intermediate-algebra-2e/pages/1-introduction
- Section URL: https://openstax.org/books/intermediate-algebra-2e/pages/9-1-solve-quadratic-equations-using-the-square-root-property

- Arts & Music
- English Language Arts
- World Language
- Social Studies - History
- Holidays / Seasonal
- Independent Work Packet
- Easel by TPT
- Google Apps

## Interactive resources you can assign in your digital classroom from TPT.

## Easel Activities

## Easel Assessments

Unlock access to 4 million resources — at no cost to you — with a school-funded subscription..

solve quadratic by square root

## All Formats

Resource types, all resource types, results for solve quadratic by square root.

## Solving Quadratic Equations by Square Roots Coloring Printable and Digital Pixel

Also included in: BACK TO SCHOOL | ALGEBRA 1 QUADRATIC EQUATIONS Bundle

## Solving Quadratic Equations (by square roots): Riddle Worksheet and Maze

Also included in: Algebra 1 Line Puzzles Activity Bundle

## Solving Quadratics by Square Roots Maze!

## Solving Quadratics by Square Roots Activity - Brazil Adventure Worksheet

Also included in: Adventure - ALGEBRA BUNDLE - Printable & Digital Activities

## Quadratic Equations Coloring Worksheet

Also included in: Quadratic Equations Activity Bundle

## Solving Quadratic Equations by Square Roots

## Solving Quadratic Equations by Completing the Square- 2 Levels-Matching Activity

Also included in: Growing Bundle~All my Algebra Activities~Quadratics~Linear~Roots~Absolute Value

## Solve Quadratics by The Square Root Method Matching Game

## EMOJI - Solve Polynomial Equations by Factoring

Also included in: EMOJI - BUNDLE Polynomial Functions

## Alg 1 -- Solving Quadratic Equations Review -- Scavenger Hunt

## Solving Quadratic Equations (All Methods) | Cut and Paste Puzzles

Also included in: Quadratic Equations Activities Bundle

## Solving Quadratic Equations Task Cards

## Solve by Completing the Square Puzzle

## Solving Quadratic Equations (with Complex Solutions) | Gone Fishin' Game

## PIXEL ART: Solve Quadratic Equation by Square Root Property L2 DISTANCE LEARNING

Also included in: BUNDLE PIXEL ART: ALGEBRA I VOLUME 3 (20 PRODUCTS) - DISTANCE LEARNING

## Solving Quadratic Equations Foldable Flip Book plus HW

Also included in: Algebra Foldables and Organizers Bundle

## Solve Quadratics by Taking the Square Root

Also included in: Solving Quadratics Digital Activities

## Solving Quadratics by Square Root Method Digital Activity

Also included in: Quadratics Mega Bundle Digital Activities

## Solving Quadratics by Square Root Method Differentiated Partner Worksheets

Also included in: Differentiated Partner Worksheets Bundle

## Solve Quadratic Equations by Taking Square Roots

Also included in: Solving Quadratic Equations

## Solving Quadratics Crazy Bingo (Solve by taking square root. Vertex form.)

## Solving Quadratic Equations - Partner Practice

## Maze - Solve Quadratic Equation by applying the Square Root Property Level 1

Also included in: Maze - MEGA BUNDLE Quadratic Functions AND Quadratic Equations

## Solve Quadratics by Graphing, Using Square Roots, Factoring NO Prep Lesson & HW

TPT empowers educators to teach at their best.

## Keep in Touch!

## Solve square root equations

There are a variety of methods that can be used to Solve square root equations.

## Square Root Equations

Math is a way of solving problems by using numbers and equations.

If you want to save time, do your research and plan ahead.

To solve a math equation, you need to find the value of the variable that makes the equation true.

## Solving square

- Do mathematic
- Solve math questions
- Clear up math problems
- More than just an application
- Obtain Help with Homework

## 9.6 Solve Equations with Square Roots

## What do our customers say?

- EXPLORE Coupons Tech Help Pro Random Article About Us Quizzes Contribute Train Your Brain Game Improve Your English Popular Categories Arts and Entertainment Artwork Books Movies Computers and Electronics Computers Phone Skills Technology Hacks Health Men's Health Mental Health Women's Health Relationships Dating Love Relationship Issues Hobbies and Crafts Crafts Drawing Games Education & Communication Communication Skills Personal Development Studying Personal Care and Style Fashion Hair Care Personal Hygiene Youth Personal Care School Stuff Dating All Categories Arts and Entertainment Finance and Business Home and Garden Relationship Quizzes Cars & Other Vehicles Food and Entertaining Personal Care and Style Sports and Fitness Computers and Electronics Health Pets and Animals Travel Education & Communication Hobbies and Crafts Philosophy and Religion Work World Family Life Holidays and Traditions Relationships Youth
- HELP US Support wikiHow Community Dashboard Write an Article Request a New Article More Ideas...
- EDIT Edit this Article
- PRO Courses New Guides Tech Help Pro New Expert Videos About wikiHow Pro Coupons Quizzes Upgrade Sign In
- Premium wikiHow Guides
- Browse Articles
- Quizzes New
- Train Your Brain New
- Improve Your English New
- Support wikiHow
- About wikiHow
- Easy Ways to Help
- Approve Questions
- Fix Spelling
- More Things to Try...
- H&M Coupons
- Hotwire Promo Codes
- StubHub Discount Codes
- Ashley Furniture Coupons
- Blue Nile Promo Codes
- NordVPN Coupons
- Samsung Promo Codes
- Chewy Promo Codes
- Ulta Coupons
- Vistaprint Promo Codes
- Shutterfly Promo Codes
- DoorDash Promo Codes
- Office Depot Coupons
- adidas Promo Codes
- Home Depot Coupons
- DSW Coupons
- Bed Bath and Beyond Coupons
- Lowe's Coupons
- Surfshark Coupons
- Nordstrom Coupons
- Walmart Promo Codes
- Dick's Sporting Goods Coupons
- Fanatics Coupons
- Edible Arrangements Coupons
- eBay Coupons
- Log in / Sign up
- Education and Communications
- Mathematics

## How to Solve Radical Equations

Last Updated: March 11, 2023 References

## Solving Equations with One Radical

## Solving Equations with Multiple Radicals

## Expert Q&A

- You must check your solutions to end up at the right answers. Not all of the answers you find when solving radical equations are actual solutions. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0
- The same steps work for cube roots, fourth roots and other roots. Instead of squaring both sides, for a cube root you will cube both sides. If you have a fourth root, you will raise both sides to the fourth power. This will work for any power. ⧼thumbs_response⧽ Helpful 0 Not Helpful 0

## You Might Also Like

- ↑ https://www.mathsisfun.com/algebra/radical-equations-solving.html
- ↑ https://www.khanacademy.org/math/algebra2/radical-equations-and-functions/solving-square-root-equations/v/solving-radical-equations
- ↑ https://www.youtube.com/watch?v=jpD_BugTR6I
- ↑ https://www.khanacademy.org/math/algebra/x2f8bb11595b61c86:quadratic-functions-equations/x2f8bb11595b61c86:untitled-1082/a/solving-quadratic-equations-by-taking-square-roots
- ↑ https://www.youtube.com/watch?v=gUh5ZNhI2lI
- ↑ https://www.youtube.com/watch?v=OSIxXgvrgC0

## About This Article

## Reader Success Stories

## Did this article help you?

## Featured Articles

## Trending Articles

## Watch Articles

Sign up for wikiHow's weekly email newsletter

## Microsoft Math Solver

## Related Concepts

## Sciencing_Icons_Science SCIENCE

## How to Solve a Square Root Equation

## How to Find the Line of Symmetry in a Quadratic Equation

## Squares and Square Roots: Basic Properties

## Square Root Terminology

This in turn is part of a general scheme:

then, represents the same number as x (5/3) from the previous paragraph does.

## Graphs of Square Root Functions

This is the case with the graph of

## Square Root Problems

Therefore, the fraction can be written

The radicals cancel each other out, and you are left with 6/3 = 2.

## Related Articles

- College of the Redwoods: The Square Root Function
- West Texas A&M University: Rationalizing Denominators and Numerators of Radical Expressions
- Desmos.com: Exponential Functions

## Find Your Next Great Science Fair Project! GO

We Have More Great Sciencing Articles!

## Accessibility links

## Solving quadratic equations

## Solving quadratic equations - Edexcel test questions - Edexcel

How do you factorise the following quadratic: x 2 - 5x - 14?

Factorise the quadratic 2x 2 + x - 3

\[x = 1\:and\:x = \frac{-3}{2}\]

\[x = \frac{3}{2}\:and\:x = -1\]

\[x = 1\:and\:x = \frac{3}{2}\]

Write x 2 + 5x in completed square form.

\[(x + \frac{5}{2})^2 - \frac{25}{4}\]

In the quadratic 2x 2 - 7x - 7 = 0, what are the values of a, b and c?

Solve 2x 2 - 7x - 7 = 0, leaving the answer in surd (square root) form.

\[x = \frac{7 \pm \sqrt{105}}{4}\]

\[x = \frac{7 \pm \sqrt{105}}{2}\]

\[x = \frac{-7 \pm \sqrt{105}}{4}\]

## GCSE Subjects GCSE Subjects up down

- Art and Design
- Biology (Single Science)
- Chemistry (Single Science)
- Combined Science
- Computer Science
- Design and Technology
- Digital Technology (CCEA)
- English Language
- English Literature
- Home Economics: Food and Nutrition (CCEA)
- Hospitality (CCEA)
- Irish – Learners (CCEA)
- Journalism (CCEA)
- Learning for Life and Work (CCEA)
- Maths Numeracy (WJEC)
- Media Studies
- Modern Foreign Languages
- Moving Image Arts (CCEA)
- Physical Education
- Physics (Single Science)
- PSHE and Citizenship
- Religious Studies
- Welsh Second Language (WJEC)

## IMAGES

## VIDEO

## COMMENTS

We can use a linear approximation to find a close estimate for the square root. √ (x) ≈ (x + y) / (2 * √ (y)) where y is a number that is "close to" x. Typically, you would choose y to be a perfect square to make the math easy. ( 3 votes) svmejia 7 years ago

If you mean x^2 = 8, then you have to transpose the square; look x^2 = 8 x = sqrt (8) x = [sqrt (4)] [sqrt (2)] // Using the product rule [ sqrt (a)*sqrt (b) = sqrt (ab)] look for perfect squares and simplify x = 2 [sqrt (2)] // sqrt (4) = 2 since 2^2 =4

Now we will see how to solve a radical equation. Our strategy is based on the relation between taking a square root and squaring. For a ≥ 0, (√a)2 = a How to Solve Radical Equations Example 8.6.4 Solve: √2x − 1 = 7 Answer Example 8.6.5 Solve: √3x − 5 = 5. Answer Example 8.6.6 Solve: √4x + 8 = 6. Answer Definition: SOLVE A RADICAL EQUATION.

Now, since 9, which is a perfect square, is separated from 100, we can take its square root on its own. √ (9 × 100) = √ (9) × √ (100) = 3 × √ (100). In other words, √ (900) = 3√ (100). We can even simplify this two steps further by dividing 100 into the factors 25 and 4. √ (100) = √ (25 × 4) = √ (25) × √ (4) = 5 × 2 = 10.

Introduction; 2.1 Solve Equations Using the Subtraction and Addition Properties of Equality; 2.2 Solve Equations using the Division and Multiplication Properties of Equality; 2.3 Solve Equations with Variables and Constants on Both Sides; 2.4 Use a General Strategy to Solve Linear Equations; 2.5 Solve Equations with Fractions or Decimals; 2.6 Solve a Formula for a Specific Variable

Key Strategy in Solving Quadratic Equations using the Square Root Method The general approach is to collect all {x^2} x2 terms on one side of the equation while keeping the constants to the opposite side. After doing so, the next obvious step is to take the square roots of both sides to solve for the value of x x.

Learn for free about math, art, computer programming, economics, physics, chemistry, biology, medicine, finance, history, and more. Khan Academy is a nonprofit with the mission of providing a free, world-class education for anyone, anywhere.

Square Roots Calculator Find square roots of any number step-by-step full pad » Examples Related Symbolab blog posts Practice, practice, practice Math can be an intimidating subject. Each new topic we learn has symbols and problems we have never seen. The unknowing... Read More

The strategy for solving is to isolate the square root on the left side of the equation and then square both sides. First subtract 2 from both sides: x − 3 = 4. Now that the square root is isolated, we can square both sides of the equation: ( x − 3) 2 = 4 2. Since the square and the square root cancel we get: x − 3 = 16.

Solve a Quadratic Equation Using the Square Root Property Isolate the quadratic term and make its coefficient one. Use Square Root Property. Simplify the radical. Check the solutions. In order to use the Square Root Property, the coefficient of the variable term must equal one.

Solve Quadratic Equations of the Form a(x − h) 2 = k Using the Square Root Property. We can use the Square Root Property to solve an equation of the form a(x − h) 2 = k as well. Notice that the quadratic term, x, in the original form ax 2 = k is replaced with (x − h). The first step, like before, is to isolate the term that has the variable squared.

This video explains how use square roots to solve quadratic equations in the form ax^2+c=0.

4.8. (33) $4.50. PDF. Students will solve 14 quadratic equations (where b=0) using square roots. There are three levels included to provide easy differentiation for your classroom (solutions as approximate values, solutions as exact values and solutions as exact values plus four multi-step equations). Two unique formats, printable coloring ...

98K views 11 years ago Solving Radical Equations This video provides two examples of how to solve a radical equations containing square roots with the variable under the square root...

Solve square root equations - We can use a linear approximation to find a close estimate for the square root. (x) (x + y) / (2 * (y)) where y is a number that. ... Square Root Equation Calculator is a free online tool that displays the variable for the given square root equation. BYJU'S online square root equation

2. Square both sides of the equation to remove the radical. All you have to do to undo a radical is square it. Because you need the equation to stay balanced, you square both sides, just like you added or subtracted from both sides earlier. So, for the example: Isolate. x {\displaystyle {\sqrt {x}}}

Solving Quadratics Quiz 2. Q. Solve the equation using square roots. Solve the equation using square roots. Use the square root property to solve the Quadratic Equation. Q. Use the square root property to solve the Quadratic Equation. Solve the equation using the zero product property.

Square Root In mathematics, a square root of a number x is a number y such that y² = x; in other words, a number y whose square (the result of multiplying the number by itself, or y ⋅ y) is x. For example, 4 and −4 are square roots of 16, because 4² = (−4)² = 16.

This in turn is part of a general scheme: x^ { (y/z)} x(y/z) means "raise x to the power of y , then take the ' z ' root of it." x 1/2 thus means "raise x to the first power, which is simply x again, and then take the 2 root of it, or the square root." Extending this, x (5/3) means "raise x to the power of 5, then find the third root (or cube ...

Solving quadratic equations. Solve quadratic equations by factorising, using formulae and completing the square. Each method also provides information about the corresponding quadratic graph. Part of.