Simplifying Radicals

Perfect Squares

1

4

9

16

25

36

49

64

81

100

121

144

169

196

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

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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

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+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

22

212210

24*325*2

2*1632*252

Simplify each expression: Simplify each radical first and then combine.

485273

229

22029

34*533*3

3*1653*93

18

288

75

24

72

=

=

=

=

=

=

=

=

=

=

Perfect Square Factor * Other Factor

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Simplify each expression

636556

547243

32782

*To multiply radicals: multiply the

coefficients and then multiply

the radicands and 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 10020 20010*20

2

5 5*5 25 5

2

7 7*7 49 7

2

8 8*8 64 8

2

x xx * 2x x

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

10

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

6

3Reduce

the

fraction.

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=