Simplifying Radicals

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

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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

Simplify each expression

20556

32718

6367282

*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

56 8 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=