Beginning Algebra, 11th Edition

Simplifying a Product of Radicals

Simplify.

Product rule

Multiply fractions.

Quotient rule

Product rule

Rationalize the denominator.

Product rule;

Multiply. NOW TRY

Simplifying Quotients Involving Radicals

Simplify. Assume that xand yrepresent positive real numbers.

(a)

= 24 = 2

22 xy

y

=

24 xy

y

=

24 x# 2 y

2 y# 2 y

24 x

2 y

EXAMPLE 4

=

215

12

= 23 # 23 = 3

215

4 # 3

=

25 # 23

423 # 23

= 216 = 4

25

423

=

25

216 # 23

=

25

248

=

B

5

48

=

B

5

8

#^1

6

B

5

8

#

B

1

6

EXAMPLE 3

SECTION 8.4 Rationalizing the Denominator 519

Product rule;

2 y# 2 y=y

Rationalize the

denominator.

(b)

Quotient rule

Product rule

=

x 26 y

3

=

2 x^226 y

3

=

26 x^2 y

3

=

22 x^2 y# 23

23 # 23

=

22 x^2 y

23

B

2 x^2 y

3

Rationalize the

denominator.

Product rule;

23 # 23 = 3

since x 7 0.

2 x^2 =x,

NOW TRY

NOW TRY
EXERCISE 3
Simplify.

B

1

6

#

B

3

10

NOW TRY
EXERCISE 4
Simplify. Assume that mand
nrepresent positive real
numbers.

(a) (b)
B

16 m^2 n

5

29 m

2 n

NOW TRY ANSWERS

3. 
   

4. (a) (b)
   4 m 25 n
   5

32 mn

n

25

10