Solving Square Root and Other Radical Equations

1
Section 7.5

• Solving Square Root and Other Radical Equations

2
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
(For help, go to Lesson 5-4.)

• Solve by factoring.
• x2 x 6
• 2. 2x2 x 3
• 3. 4x2 8x 5

x 3 or x 2
Check Skills Youll Need
7-5
3
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
Solve 10 2x 1 5.
2x 1 25 2x 24 x 12
Quick Check
7-5
4
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
3 5
Solve 3(x 1) 24.
x 1 32 Simplify. x 31
Quick Check
7-5
5
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
An artist wants to make a plastic sphere for a
sculpture. The plastic weighs 0.8 ounce per cubic
inch. The maximum weight of the sphere is to be
80 pounds. The formula for the volume V of a
sphere is V r 3, where r is the radius
of the sphere. What is the maximum radius the
sphere can have?
4 3
7-5
6
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
(continued)
0.8 80
The maximum radius is about 2.88 inches.
Quick Check
7-5
7
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
Solve x 2 3 2x. Check for extraneous
solutions.
7-5
8
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
(continued)
Check x 2 3 2x x 2 3 2x
1 2 3 2(1) 2 3 2
1 3 2
3 2 2 3
1 4
1 2

/
The only solution is 1.
Quick Check
7-5
9
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
2 3
1 3
Solve (x 1) (9x 1) 0. Check for
extraneous solutions.
x 0 or x 7
7-5
10
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
(continued)
Check (x 1) (9x 1) 0 (x 1)
(9x 1) 0 (0 1) (9(0) 1)
0 (7 1) (9(7) 1) 0 (1)
(1) 0 (8) (64 )
0 (1) (12) 0
(8) (82) 0 1
1 0 8 8 0

1 3
2 3
1 3
2 3
2 3
1 3
1 3
2 3
2 3
1 3
1 3
2 3
2 3
1 3
1 3
2 3
2 3
2 3
2 3
2 3
Both 0 and 7 are solutions.
Quick Check
7-5
11
Solving Square Root and Other Radical Equations
ALGEBRA 2 LESSON 7-5
5
17
13
about 2.34 ft
7-5