1. 3.6 Solving Quadratic Equations
By Finding the Square Root

2. Simplifying Expressions with Radicals
Perfect Square can’t be in radical
Fraction can’t be in radical
Radical can’t be in the denominator
Rationalize the denominator
To add/subtract, you must have like radicands

3. 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

4. GUIDED PRACTICE
GUIDED PRACTICE 27 10 15 9 64
ANSWER
ANSWER
ANSWER
3 8 3 6 5 8 28 15 4 98
ANSWER 2 15
ANSWER
ANSWER 14 4 2 7 36 49 11 25 7 6 5 11

5. EXAMPLE 2
Rationalize denominators of fractions. 5 2 3
7 + 2
Simplify
(a)
and
(b)
SOLUTION = 3
7 + 2
7 –
(a) 5 2 = 5 2
(b) 3
7 + 2 = 5 2 =
21 – 3 2
49 – – 2 2 10 = =
21 – 3 2 47

6. Key to solving using square roots
Remember—You have to include the positive (principle) root as well as the negative root.
x2 = 121
x = ± 11

7. 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.

8. 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 

9. 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

10. GUIDED PRACTICE
GUIDED PRACTICE
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

11. GUIDED PRACTICE
– 1
9 + 7
– 9 + 7 74
ANSWER 4
8 – 3
32 + 4 3 61
ANSWER

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