Page 729 - Algebra 1

Sometimes the radical is not isolated in a radical equation. In those cases, inverse operations for addition, subtraction, multiplication, and division can be used to isolate the radical. Once the radical has been isolated, both sides of the equation can be squared.
Solving by Isolating the Square Root
Example
2
Solve each equation.
a. √x -5=8 SOLUTION
Use inverse operations.
b. √x +5=8 SOLUTION
Use inverse operations.
Math Reasoning
Analyze Is squaring first helpful in solving the
e q u a t i o n √ x - 5 = 8 ?
√ x - 5 = 8 +_ _5 = +_ _5
Check √x -5=8 √ 16 9 - 5 8
√ x + 5 = 8 -__5 = -__5
√x = 3
√ x = 1 3 (√x)2 = 132
Addition Property of Equality
Simplify.
Square both sides. Simplify.
2 2 (√x) =3
Subtraction Property of Equality
Simplify.
Square both sides. Simplify.
✓
C h e c k

x = 169
x=9

x = 49
x = 1296 _√ x = 1 8
_2 √ 129 6 18
√ 9 + 5 8 13-5 8 3+5 8
8=8 ✓ c. 3 √ x = 21
SOLUTION
Use inverse operations.
8=8 d. _√ x = 18
2
SOLUTION
_√x = 18 2
√x +5=8
_3 √ x = 2 1
_21 3=3
√ x = 7
22 (√x) =7
_
√x · 2 = 18 · 2
3√x
Division Property of Equality
Simplify.
Square both sides. Simplify.
3 √ x = 2 1
3√ 49 21
3 · 7 21 21=21 ✓
__
Multiplication Property of Equality
Simplify.
Square both sides. Simplify.
2 1
√ x = 3 6
(√x)2 = 362
1
2
_36 18 2
18=18 ✓
714 Saxon Algebra 1