Simplifying Radicals

To make some extra cash, Bill Shakespeare

works as a substitute math teacher.

Perfect Squares

1

4

9

16

25

36

49

64

81

100

121

144

169

196

225

256

324

400

625

289

361

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

18

288

24

72

=

=

=

=

=

=

=

=

Perfect Square Factor * Other Factor

LE

AV

E I

N R

AD

ICA

L F

OR

M

2*9 23

2*144 212

6*4 62

2*36 26

+

To combine

radicals:

combine the

coefficients of

like radicals

Simplify each expression

737576 78

62747365 7763

Simplify each expression: Simplify each radical first and

then combine.

323502 2*1632*252

24*325*2

212210

22

Simplify each expression: Simplify each radical first and

then combine.

485273

22922029

34*533*3

3*1653*93

How much is 2 + 82

dollars?

= 2 + 4 ∗ 22

= 2 + 2 22

= 3 22= 32 2

2= 9 ∗ 2 = 18

Worksheet

Problems 1-10

*To multiply radicals:

multiply the

coefficients, then

multiply the radicands,

then simplify the

remaining radicals.

35*5 175 7*25 75

Multiply and then simplify

73*82 566 14*46

142*6 1412

204*52 1008 8010*8

2

5 5*5 25 5

2

7 7*7 49 7

2

8 8*8 64 8

2

x xx * 2x x

Worksheet

Problems 11-16

To divide radicals: divide the coefficients,

divide the radicands if possible, and

rationalize the denominator so that no

radical remains in the denominator

7

568 2*4 22

7

6This cannot be

divided which leaves

the radical in the

denominator. We do

not leave radicals in

the denominator. So

we need to

rationalize by

multiplying the

fraction by something

so we can eliminate

the radical in the

denominator.

7

7*

7

6

49

42

7

42

42 cannot be

simplified, so we are

finished.

This can be divided

which leaves the

radical in the

denominator. We do

not leave radicals in

the denominator. So

we need to

rationalize by

multiplying the

fraction by something

so we can eliminate

the radical in the

denominator.

10

5

2

2*

2

1

2

2

This cannot be

divided which leaves

the radical in the

denominator. We do

not leave radicals in

the denominator. So

we need to

rationalize by

multiplying the

fraction by something

so we can eliminate

the radical in the

denominator.

12

3

3

3*

12

3

36

33

6

33

2

3Reduce

the

fraction.

Worksheet

Problems 17-22