11-3Simplifying Radical Expressions

Standard 2.0One Property

CA Standard 2.0

Understand and use the operation of taking a root.

Product Properties for Radicals

For any nonnegative real numbers x and y.

yxxy a.

b.

xxx

Using the Product Properties

1.

2.

3.

4.

1.

2.

3.

4.

125

767

449

67

1243

60

25511 555555

Rules for Radical Expressions

a. Simplify the radicand first

b. When odd powers occur, express the power as the product of the largest even power and your exponential base.

c. Simplify your perfect squares.

#5 Simplify

32

2 16 4

24

#6 Simplify

45

5 9 3

53

#7 Simplify

96

16 6

64

2 3 6

#8 Simplify

216

2 108

66

2 54

6 9

#9 Simplify

All even powers are perfect squares.

8y

21

8y

4y

#10 Simplify

14)( yx

21

14yx

7yx

#11 Simplify

x60

x154

x152

#12 Simplify

240y

2104 y

102y

#13 Simplify

Express odd powers as the product of the largest even power and your exponential base.

15a

aa 21

14

aa7

aa14

#14 Simplify

25m

mm 21

24

mm12

mm24

#15 Simplify

7147 2 xx

)12(7 2 xx

2)1(7 x

17 x

2)1(7 x