Math 025 Section 10.1

Radicals

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

Simplified radical form

18 = 9

2

3

2

=

108 = 36

3

6

3

=

396 = 316

6

12

6

=

No factor inside the radical should be a perfect square.

Simplifying variable radical expressions

x6 x3=

x15 = x14 x

x7

x

=

x9 = x8

x

4x4

x

=

A variable with an even exponent is a perfect square

4 4

Simplifying radical expressions

16x7 4x3=

5xx3y4 = x2

y4

x

5x2y2

x

=

96x5y7 = 16x4y6

6xy

4x2y3 6xy =

Simplify each of the following

= 16x6 x

x

5x

Simplifying radical expressions

81(x – 2)2 9(x – 2) =

x2 + 6x + 9 (x + 3)2 = x + 3 =

Simplify each of the following

9x – 18 =

( )