1.1 SIMPLIFYING RADICALSSec Math 2

SIMPLIFYING RADICALS

Methods for Simplifying Radical Expressions

Two Methods for Simplifying Radical Expressions:

1. Simplify by finding perfect squares

2. Simplify by creating a factor tree

1. Simplify by finding perfect squares

PERFECT SQUARES

1

4

916

253649

64

81

100121

144169196

225

256

324

400

625

289

4

16

25

100

144

= 2

= 4

= 5

= 10

= 12

8

20

32

75

40

=

= =

=

=

2*4

5*4

2*16

3*25

10*4

=

=

=

=

=

22

52

24

35

102

Perfect Square Factor * Other Factor

LE

AV

E I

N R

AD

ICA

L F

OR

M

48

80

50

125

450

=

= =

=

=

3*16

5*16

2*25

5*25

2*225

=

=

=

=

=

34

54

225

55

215

Perfect Square Factor * Other Factor

LE

AV

E I

N R

AD

ICA

L F

OR

M

2. Simplify by creating a factor tree

Step 1.  Factor the number under the radical sign into prime numbers

48 = 2 ∙ 24

2 ∙ 12

2 ∙ 6

2 ∙ 3

Prime numbers of 48 = 2 ∙ 2 ∙ 2 ∙ 2 ∙ 3

Simplify or Reduce a Radical by Finding Prime Factors

48Reduce

Step 2.  Group prime numbers into squares

Step 3.  Reduce the radical from the perfect squares

Step 4. Simplify the radical.

48 2 2 2 2 3

2 22 2 3

32 2

4 3

Simplify or Reduce a Radical by Finding Prime Factors

Simplify Each Expression

Simplify 72Method 1: Finding Perfect Squares Method 2: Factor into Prime Numbers

72 2 36

2 36

6 2

72 2 36

2 18

2 9

3 3

72 2 2 2 3 3 2 272 2 2 3

72 2 3 2

= 6 2

A radical expression is in simplest form when all the following are true.

Simplify or Reduce a Radical

Simplify the expression

5 10

5 10 5 10

5 2 5

5 2

2X

6Y

264 YXP

244 YX

10825 DC

= X

= Y3

= P2X3Y

= 2X2Y

= 5C4D10

3X

XX

=

=

XX *2

YY 45Y

=

= YY 2

33YPX

2712 YX

9825 DC

=

=

= 5Y

PXYYX *22

5Y

PXYXY=

Please Do you homework Worksheet:

1.1 Simplifying Radicals