1. 4.5 Solve Quadratic Equations by Finding Square Roots

2. EXAMPLE 1
Use properties of square roots
Simplify the expression. a. 80 5 16 = 5
= 4 b. 6 21
126 = 9 14 =
= 3 14 c. 4 81 = 4 81 =
2 9 d. 7 16 = 7 16 = 4 7

3. GUIDED PRACTICE
GUIDED PRACTICE
for Example 1 27
ANSWER 3 98
ANSWER 2 7

4. GUIDED PRACTICE
GUIDED PRACTICE
for Example 1 10 15
ANSWER 6 5 8 28
ANSWER 14 4

5. GUIDED PRACTICE
GUIDED PRACTICE
for Example 1 9 64
3 8
ANSWER 15 4 2 15
ANSWER

6. GUIDED PRACTICE
GUIDED PRACTICE
for Example 1 11 25 5 11
ANSWER 36 49 7 6
ANSWER

7. EXAMPLE 2
Rationalize denominators of fractions. 5 2 3
7 + 2
Simplify
(a)
and
(b)
SOLUTION
(a) 5 2 = 5 2 = 5 2 2 10 =

8. EXAMPLE 2
Rationalize denominators of fractions.
SOLUTION = 3
7 + 2
7 –
(b) 3
7 + 2 =
21 – 3 2
49 – – 2 =
21 – 3 2 47

9. Solve a quadratic equation
EXAMPLE 3
Solve a quadratic equation
Solve 3x2 + 5 = 41.
3x2 + 5 = 41
Write original equation.
3x2 = 36
Subtract 5 from each side.
x2 = 12
Divide each side by 3.
x = + 12
Take square roots of each side.
x = + 4 3
Product property
x =
+ 2 3
Simplify.

10. Solve a quadratic equation
EXAMPLE 3
Solve a quadratic equation
ANSWER
The solutions are and 2 3 2 3 –
Check the solutions by substituting them into the original equation.
3x2 + 5 = 41
3x2 + 5 = 41
3( )2 + 5 = 41 2 3 ?
3( )2 + 5 = 41
– 2 3 ?
3(12) + 5 = 41 ?
3(12) + 5 = 41 ?
41 = 41 
41 = 41 

11. Standardized Test Practice
EXAMPLE 4
Standardized Test Practice
SOLUTION 15
(z + 3)2 = 7
Write original equation.
(z + 3)2 = 35
Multiply each side by 5.
z + 3 = + 35
Take square roots of each side.
z = –3 + 35
Subtract 3 from each side.
The solutions are – and –3 – 35

12. EXAMPLE 4
Standardized Test Practice
ANSWER
The correct answer is C.

13. GUIDED PRACTICE
GUIDED PRACTICE
for Examples 2, 3, and 4
Simplify the expression. 6 5 19 21 5 30
399 21
ANSWER
ANSWER 9 8
– 6
7 – 5 2 4 3
– 21 – 3 5 22
ANSWER
ANSWER 17 12 2
4 + 11 51 6
ANSWER
8 – 2 11 5
ANSWER

14. GUIDED PRACTICE
for Examples 2, 3, and 4
– 1
9 + 7
– 9 + 7 74
ANSWER 4
8 – 3
32 + 4 3 61
ANSWER

15. GUIDED PRACTICE
for Examples 2, 3, and 4
Solve the equation.
5x2 = 80
ANSWER
+ 4
z2 – 7 = 29
+ 6
ANSWER
3(x – 2)2 = 40
120 3 2 +
ANSWER