6-5
PART 2
Solving Square Root and
Other Radical Equations
Vocabulary
Review
1. Draw a line from each square root expression in Column A to an equivalent
expression in Column B.
Column A
Column B
!100
10!x
!100x
10
"100x 2
10!10
!1000
10u x u
2. Circle the square root equation that is equivalent to !x 2 2 5 4.
!x 2 2 5 4
!x 2 1 5 5
!x 2 2 1 7 5 11
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Vocabulary Builder
eliminate (noun) ee LIM uh nayt
Definition: To eliminate something is to remove or get rid of it.
Math Usage: To eliminate a term in an equation, use the inverse operation.
Main Idea: To isolate a variable term in an equation, use inverse operations, doing
the same thing to each side of the equation to keep it true.
Use Your Vocabulary
3. To eliminate the 3 from x 1 3 5 5, add 3 to / subtract 3 from each side.
4. To eliminate the 6.7 from t 2 6.7 5 5, add 6.7 to / subtract 6.7 from each side.
5. To eliminate the 4 from 4y 5 252, multiply / divide each side by 4.
6. To eliminate the radical in !z 2 1 5 10, square / take the square root of each side.
s
7. To eliminate the 17 in the equation 17
5 0.5, multiply / divide each side by 17.
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Lesson 6-5, Part 2
4/9/09 10:08:59 AM
Solving a square root equation may require that you square each side of the
equation. This can introduce extraneous solutions.
Problem 4
Checking for Extraneous Solutions
Got It? What is the solution of !5x 2 1 1 3 5 x? Check your results.
8. Use the justifications at the right to complete each step.
!5x 2 1 1 3 5 x
Write the original equation.
!5x 2 1 5 x 2
Isolate the radical.
( !5x 2 1)2 5
Square each side of the equation.
5x 2 1 5 x 2 1
x1
Simplify.
0 5 x2 2
x1
Combine like terms.
0 5 Qx 2
R Qx 2
x5
or x 5
R
Factor.
Use the Zero-Product Property.
9. Substitute each value into the original equation to check the solutions.
"5Q
R21 1301
"
10. The solution
!5x 2 1 1 3 5 x
"5Q
R 2 1 1 3 0 10
"
1301
1 3 0 10
1301
1 3 0 10
01
5 10
is extraneous.
11. Multiple Choice What can cause an extraneous solution?
raising each side of the equation to an odd power
raising each side of the equation to an even power
adding the same number to each side of an equation
dividing each side of an equation by the same number
12. When should you check for extraneous solutions? Explain.
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!5x 2 1 1 3 5 x
Problem 5 Solving an Equation With Two Radicals
Got It? What is the solution of !5x 1 4 2 !x 5 4?
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13. The equation has been solved below. Write the letter of the reason that justifies
each step. Use the reasons in the box.
A Addition Property of Equality
!5x 1 4 5 !x 1 4
B Square each side.
5x 1 4 5 ( !x 1 4)2
C Division Property of Equality
5x 1 4 5 x 1 8!x 1 16
D Factor.
E Simplify.
4x 2 12 5 8!x
F Zero-Product Property
x 2 3 5 2!x
(x 2 3)2 5 4x
x 2 2 6x 1 9 5 4x
x 2 2 10x 1 9 5 0
(x 2 9)(x 1 1) 5 0
x 5 9 or x 5 21
14. Only the solution x 5 21 > x 5 9 satisfies the original equation.
Lesson Check • Do you UNDERSTAND?
Vocabulary Which value, 12 or 3, is an extraneous solution of x 2 6 5 !3x?
Explain your reasoning.
Copyright © by Pearson Education, Inc. or its affiliates. All Rights Reserved.
15. The solution x 5 12 satisfies / does not satisfy the original equation. The solution
x 5 3 satisfies / does not satisfy the original equation.
16. The solution x 5 12 > x 5 3 is an extraneous solution of x 2 6 5 !3x.
17. Explain why the solution is extraneous.
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Math Success
Check off the vocabulary words that you understand.
radical equation
square root equation
Rate how well you can solve square root and other radical equations.
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Lesson 6-5, Part 2
4/9/09 10:09:30 AM