Akar dan Radikal

(Square Roots and Radical)

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: Estimating 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

A. 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 =

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

B. 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.

Just in case you forgot..Just in case you forgot..

The Real Number LineThe Real Number Line

is next..is next..

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

HAL-HAL PENTINGHAL-HAL PENTING

A.A. Mengalikan AkarMengalikan Akar

B.B. Menyederhanakan Bentuk AkarMenyederhanakan Bentuk Akar

C.C. Merasionalisasikan Pecahan AkarMerasionalisasikan Pecahan Akar

D.D. Akar ke-n.Akar ke-n.

A. 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 =

B. 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.

C. Rationalizing Improper FractionsC. Rationalizing Improper Fractions

Multiply the fractions with its Multiply the fractions with its corresponding “Akar Sekawan”corresponding “Akar Sekawan”

D. Akar ke-nD. Akar ke-n