The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Name Date

WORKSHEET 8.18: SOLVING RADICAL EQUATIONS

-------------------------------------------------------------------------------------

Follow the steps below to solve radical equations:

1. Isolate the radical.


2. Square both sides of the equation. This will eliminate the radical symbol.


3. Solve.


4. Check the solution by substituting the value in the original equation.

EXAMPLES

Solve.

√

x+ 3 = 5

√

√^2 x+^4 =−^2

x= 2

√

2 x=− 6 The square root of any number must be≥0.

(

√

x)^2 = 22 There is no real solution.

x= 4

Check:

√

4 + 3 = 5

2 + 3 = 5

DIRECTIONS: Solve each equation.

√

x+ 5 = 8 2.

√

x− 4 = 0

3. 2

√

x+ 10 = 6 4.

√

x+ 7 − 4 = 21

5. 4 −

√

x+ 3 =− 2 6.

√

2 x− 5 = 7

7. 10 +

√

3 x+ 4 = 20 8. 15 −

√

3 x+ 1 = 5

CHALLENGE:Jimmy looked at the equation−

√

x+ 2 =−4. He said that there

is no real solution because the radical equals−4 and square roots are

always positive. Do you agree? Explain your reasoning.

309

Copyright

©

2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.