Holt Algebra 1

11-9 Solving Radical Equations

Warm Up 4-22-09Solve each equation.1. 3x +5 = 172. 4x + 1 = 2x – 3 3. 4. (x + 7)(x – 4) = 05. x2 – 11x + 30 = 06. x2 = 2x + 15

4–2

35–7, 4 6, 5

5, –3

Holt Algebra 1

11-9 Solving Radical Equations

Solve radical equations.Objective

Holt Algebra 1

11-9 Solving Radical Equations

radical equationextraneous solution

Vocabulary

Holt Algebra 1

11-9 Solving Radical Equations

A radical equation is an equation that contains a variable within a radical. In this course, you will only study radical equations that contain square roots.

Recall that you use inverse operations to solve equations. For nonnegative numbers, squaring and taking the square root are inverse operations. When an equation contains a variable within a square root, square both sides of the equation to solve.

Holt Algebra 1

11-9 Solving Radical Equations

Holt Algebra 1

11-9 Solving Radical Equations

Directions: Solve the equation. Check your answer.

Holt Algebra 1

11-9 Solving Radical EquationsExample 1

x = 25

55 5

Check

Holt Algebra 1

11-9 Solving Radical EquationsExample 2

100 = 2x50 = x

Check

10 10

Holt Algebra 1

11-9 Solving Radical EquationsExample 3

3x = 1

Check

Holt Algebra 1

11-9 Solving Radical Equations

Some square-root equations do not have the square root isolated. To solve these equations, you may have to isolate the square root before squaring both sides. You can do this by using one or more inverse operations.

Holt Algebra 1

11-9 Solving Radical EquationsExample 4

x = 81Check

9 – 4 55 5

Holt Algebra 1

11-9 Solving Radical EquationsExample 5

x = 46Check

7 7

Holt Algebra 1

11-9 Solving Radical EquationsExample 6

5x + 1 = 165x = 15

x = 3

Holt Algebra 1

11-9 Solving Radical EquationsExample 6 Continued

4 + 6 1010 10

Check

Holt Algebra 1

11-9 Solving Radical EquationsExample 7

Method 1

x = 64

Holt Algebra 1

11-9 Solving Radical EquationsExample 7 Continued

Method 2

x = 64

Holt Algebra 1

11-9 Solving Radical EquationsExample 7 Continued

32 32

Check

Holt Algebra 1

11-9 Solving Radical EquationsExample 8

Method 1

144 = x

Holt Algebra 1

11-9 Solving Radical EquationsExample 8 Continued

Method 2

144 = x

Holt Algebra 1

11-9 Solving Radical EquationsExample 8 Continued

12 12

Check

Holt Algebra 1

11-9 Solving Radical EquationsExample 9

Method 1

x = 100

Holt Algebra 1

11-9 Solving Radical EquationsExample 9 Continued

Method 2

4x = 400x = 100

Holt Algebra 1

11-9 Solving Radical EquationsExample 9 Continued

Check

4 4

4

Holt Algebra 1

11-9 Solving Radical EquationsLesson Summary

Solve each equation. Check your answer.

1.

3.

2.

4.

36 45

no solution 11