1. Warm Up Simplify each expression. 1. 6² 36 2. 112 121 25 36
3. (–9)(–9) 81 4.
Write each fraction as a decimal. 2 5 5 9 5.
0.4 6.
0.5 5 3 8 –1 5 6 7.
5.375 8.
–1.83

2. Square Roots
Vocabulary & Notes

3. Vocabulary Objectives square root rational numbers
perfect square irrational numbers
real numbers repeating decimal
natural numbers terminating decimal
whole numbers Integers
Objectives
Evaluate expressions containing square roots.
Classify numbers within the real number system.

4. Square Roots
A number that is multiplied by itself to form a product is called a square root of that product. The operations of squaring and finding a square root are inverse operations.
The radical symbol , is used to represent square roots. Positive real numbers have two square roots.
4  4 = 42 = 16
= 4
Positive square
root of 16
(–4)(–4) = (–4)2 = 16
Negative square root of 16 –
= –4

5. Perfect Squares
The nonnegative square root is represented by The negative square root is represented by –
A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table. 1 4 9 16 25 36 49 64 81
100 02 12 22 32 42 52 62 72 82 92
102

6. The expression does not represent
a real number because there is no real number that can be multiplied by itself to form a product of –36.
Reading Math

7. Finding Square Roots of Perfect Squares
Find each square root. A.
Think: What number squared equals 16?
42 = 16
Positive square root positive 4.
= 4 B.
Think: What is the opposite of the square root of 9?
32 = 9
= –3
Negative square root negative 3.

8. Finding Square Roots of Perfect Squares
Find the square root.
Think: What number squared equals ? 25 81
Positive square root positive 5 9

9. Find the square root. 1a. 22 = 4 = 2 1b. 52 = 25
Try This!
Find the square root.
1a.
22 = 4
Think: What number squared equals 4?
= 2
Positive square root positive 2.
1b.
Think: What is the opposite of the square root of 25?
52 = 25
Negative square root negative 5.