Chapter 4 Lesson 4.5

By definition 25 is the number you would multiply times itself to get 25 for an answer.

Because we are familiar with multiplication, we know that 25 = 5

Numbers like 25, which have whole numbers for their square roots, are called perfect squares

You need to memorize at least the first 15 perfect squares

Perfect square

Square root

1 1 = 1

4 4 = 2

9 9 = 3

16 16 = 4

25 25 = 5

36 36 = 6

49 49 = 7

64 64 = 8

81 81 = 9

100 100 = 10

121 121 = 11

144 144 = 12

169 169 = 13

196 196 = 14

225 225 = 15

Perfect square

Square root

Every whole number has a square root

Most numbers are not perfect squares, and so their square roots are not whole numbers.

Most numbers that are not perfect squares have square roots that are irrational numbers

Irrational numbers can be represented by decimals that do not terminate and do not repeat

The decimal approximations of whole numbers can be determined using a calculator

Obj: To find the square root of a number

• Find the square roots of the given numbers

• If the number is not a perfect square, use a calculator to find the answer correct to the nearest thousandth.

81

37

158

81 = 9

37 6.083

158 12.570

Obj: To find the square root of a number

• Find two consecutive whole numbers that the given square root is between

• Try to do this without using the table

18

115

18 is between 4 and 5

115 is between 10 and 11

16 = 4 and 25 = 5 so

100 = 10 and 121 = 11 so

Multiplying radicals

The product of the square roots of two numbers is the same as the square root of the product of the

numbers

123 36

Examples:

=

117 77 =

= 6

Simplify the following expressions

49

764 + 9

-4

255 +

= -(2)

= 7 8 + 9

= 56 + 9 = 65

= 5 5 + 7

= 25 + 7 = 32

Simplify the following expressions

= 4

81

2

9

4

81=

1

36 1

144– =

1

6

1

12–

=2

12

1

12–

=1

12

Rationalizing the DenominatorWhen the radical in the denominator is not a

perfect squareA form of 1

A form of 1

A form of 1

Simplify integers

Simplify integers

Simplified radical form

18 = 9 2 = 9

2

3

2

=

108 = 36 3 = 36

3

6

3

=

96 = 16 6 = 16

6

4

6

=

No factor inside the radical should be a perfect square.

Graphing real numbers

The graph of a number is a dot placed where the number would be on the number line

0 5 10-5-10

Graph the number: 312

0 5 10-5-10

Graph the number: -8.5

Graphing inequalities

The symbol, [ , means that the point is included in the graph

0 5 10-5-10

Graph the real numbers between -4 and 6

0 5 10-5-10

Graph the real numbers less than 8

The symbol, ( , means that the point is not included in the graph

(

)

)

Graphing inequalities

The symbol, [ , means that the point is included in the graph

0 5 10-5-10

Graph the inequality: x > -3

0 5 10-5-10

Graph the inequality: x 4

The symbol, ( , means that the point is not included in the graph

(

]