Square Roots and Cube Roots

4.6

Perfect Squares

• 1• 4• 9• 16• 25

• 36• 49• 64• 81• 100

• 121• 144• 169• 196• 225

Square Root

• A square root of a number is one of its two equal factors.

• Notation: radical sign is used to indicate a nonnegative square root.

Positive and Negative Signs

36 636 1 36 6 36 6

36 no real solution

Find each square root

1.) 64

8

2.) 121

11

3.) 256

164.) 9

no real solution

Estimate to the Nearest Integer

• For numbers that are not perfect squares, find the two perfect square the number is between.

• Graph the square root on the number line to determine which perfect square it is closest to.

Estimate the nearest Integer

1.) 60

49 60 64

7 60 8

8

2.) 1816 18 25

4 18 5

4

Cube Roots

• A cube root of a number is one of its three equal factors

• If then3x y 3 y

Perfect Cube Roots

•1•8•27•64

•125•216•343•512

•729•1000

Every Integer has exactly one cube root

• The cube root of a positive number is positive• The cube root of zero is zero• The cube root of a negative number is

negative

Find the Cube Root

31.) 125

5

32.) 729

9

Estimate to the nearest integer

31.) 723 3 364 72 125

34 72 5

4

32.) 393 3 327 39 64

33 39 4

3

Homework

Page 172 (16-38) even