Roots

Lesson #8

Pg. 231

Simplify each expression.

1) 6² 36 2) 112 121

3) (–9)(–9) 81 4) 25

36Write each fraction as a decimal.

5) 25

596)

7)5 38

8)–1 56

0.4

5.375

0.5

–1.83

Warm Up

Square Root/Cube Root Rational Numbers

Perfect Square /Perfect Cube Irrational Numbers

Natural Numbers Real Numbers

Whole Numbers Repeating Decimal (Rational Number)

Integers Terminating Decimal (Rational Number)

Vocabulary

ObjectivesEvaluate expressions containing square and cube roots.

Classify numbers within the real number system.

2 or 3

2 equal factors

multiplied together

3 equal factors

multiplied together

Index of 2 Index of 3

** Counting Numbers

** 1, 2, 3, 4, …

** Counting Numbers plus zero** 0, 1, 2, 3, 4, …

** Natural, and Whole plus Negatives** … - 4, - 3, - 2, - 1, 0, 1, 2, 3, 4, …

** Natural, Whole, Integers and any number that can be put into a ratio (fraction) * Repeating or Terminating decimals

** Non – Repeating, Non – Terminating decimals

** Any number (value) on the number-line

1.333333... .3

3

3.3

10

The Real Number SystemEvery point (value) on the number line

Irrational #s

• Decimals that do not repeat or end

• Can not be written as a ratio

Rational #s• Can be written as a ratio• Decimal that repeats or ends

Integers • Tic marks on number line• …-2, -1, 0, 1, 2…

Whole #s0, 1, 2, 3…

Natural #s1, 2, 3 …

What You’ll Learn

Finding the square roots of perfect squares

Finding the cube roots of perfect cubes

Solving equations involving squares and cubes

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

• Example52 = 25, so 5 is the square root of 25

The radical symbol , is used to represent square roots. Positive real numbers have two square roots.4 4 = 42 = 16

Square Roots

= 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.

1

12

1004

22

9

32

16

42

25

52

36

62

49

72

64

82

81

92 102

The positive square root is represented by . The negative square root is represented by – .The positive and negative is represented by ± .

Perfect Squares

400

202

361

192

121

112

144

122

169

132

196

142

225

152

256

162

289

172

324

182

Examples64 1.21

25

36 16

Solving Examples2289 a 2 0.09m

2 4

25y

Cube Roots A cube root of a number is one of it’s

three equal factors Be careful, you can find the cube root of a

negative under the radical

Numbers such as 8, 27, and 64 are perfect cubes because they are the cubes of integers

38 2 2 2 or 2 g g 327 3 3 3 or 3 g g 364 4 4 4 or 4 g g

Examples3 125

3 27

Solving Examples3125 s

38 s

HOMEWORK

All Classes

Pg. 235-2361-23 all

Test Corrections due Thursday