Simplify each expression.

1. 6² 36 2. 112 121

3. (–9)(–9) 81 4.25

36

Write each fraction as a decimal.

5. 25

596.

7. 5 38

8. –1 56

0.4

5.375

0.5

–1.83

Vocabulary & Notes

square root rational numbersperfect square irrational numbersreal numbers repeating decimalnatural numbers terminating decimalwhole numbers Integers

Evaluate expressions containing square roots.

Classify numbers within the real number system.

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 squareroot of 16

(–4)(–4) = (–4)2 = 16 = –4 Negative square root of 16

–

A perfect square is a number whose positive square root is a whole number. Some examples of perfect squares are shown in the table.

0

02

1

12

1004

22

9

32

16

42

25

52

36

62

49

72

64

82

81

92 102

The nonnegative square root is represented by . The negative square root is represented by – .

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

Reading Math

Finding Square Roots of Perfect Squares

Find each square root.

42 = 16

32 = 9

Think: What number squared equals 16?

Positive square root positive 4.

Think: What is the opposite of the square root of 9?

Negative square root negative 3.

A.

= 4

B.

= –3

Find the square root.

Think: What number squared equals ?25

81

Positive square root positive .5

9

Finding Square Roots of Perfect Squares

Find the square root.

Try This!

22 = 4 Think: What number squared equals 4?

Positive square root positive 2. = 2

52 = 25

Think: What is the opposite of the square root of 25?

1a.

1b.

Negative square root negative 5.