Beginning Algebra, 11th Edition

Using the Quotient Rule to Simplify Radicals

Use the quotient rule to simplify each radical.

EXAMPLE 4

SECTION 8.2 Multiplying, Dividing, and Simplifying Radicals 507

Quotient Rule for Radicals

If aand bare nonnegative real numbers and then

and

That is, the square root of a quotient is the quotient of the two square roots, and

the quotient of two square roots is the square root of the quotient.

2 a

2 b



B

a

b

.

B

a

b



2 a

2 b

bZ0,

NOW TRY
EXERCISE 4
Simplify each radical.

(a) (b)

(c)
B

11

49

2245

B 25

81

100

NOW TRY
EXERCISE 5
Simplify.

24239

4213

(a)

=

5

3

=

225

29

B

25

9

(b)

= 12

= 2144

=

B

288

2

2288

22

(c)

=

23

2

=

23

24

B

3

4

Using the Quotient Rule to Divide Radicals

Simplify.

Multiplication of fractions

Quotient rule

= 325 Divide. NOW TRY

=

27

9

#

B

15

3

=

27

9

#^215

23

27215

923

EXAMPLE 5

NOW TRY
EXERCISE 6
Simplify.

B

1

2

#

B

5

18

NOW TRY ANSWERS

4. (a) (b) 7 (c)


5. 
   
   
   
   6. 25
   
   
   
   

(^6236)
211
7
9
10
OBJECTIVE 3 Simplify radicals by using the quotient rule.The quotient
rule for radicalsis similar to the product rule.
Using Both the Product and Quotient Rules
Simplify.
Product rule
Multiply fractions.
or Quotient rule; 225 = 5 NOW TRY

23

5

=

23

225

,

=

B

3

25

=

B

3

5

#^1

5

B

3

5

#

B

1

5

EXAMPLE 6

NOW TRY