OBJECTIVE 4 Write radical quotients in lowest terms.
Writing Radical Quotients in Lowest TermsWrite each quotient in lowest terms.
(a)
Factor the numerator and denominator.Divide out the common factor.Here is an alternative method for writing this expression in lowest terms.
6 + 225
4
=
6
4
+
225
4
=
3
2
+
25
2
=
3 + 25
2
=
3 + 25
2
=
(^2) A 3 + (^25) B
2 # 2
6 + 225
4
EXAMPLE 6
SECTION 8.5 Multiplying and Dividing Radical Expressions 463
NOW TRY
EXERCISE 6
Write each quotient in lowest
terms.
(a)
(b) k 70
15 k+ 250 k^2
20 k,
15 - 622
18
In calculus, it is sometimes desirable to rationalize the numerator.For example, to
rationalize the numerator of
we multiply the numerator and the denominator by the conjugate of the numerator.
For Discussion or Writing
Rationalize the numerator of each expression. (aand bare nonnegative real numbers.)
1. 2. 3.
4. Rationalize the denominator of the expression in Exercise 3,and then describe
the difference in the procedure you used from what you did in Exercise 3.
1 bZ a 2
32 a+ 2 b
2 b- 2 a
32 a+ 2 b
b
825 - 1
6
6 - 22
4
=
A 6 - 22 BA 6 + 22 B
(^4) A 6 + (^22) B
=
36 - 2
(^4) A 6 + (^22) B
=
34
(^4) A 6 + (^22) B
=
17
(^2) A 6 + (^22) B
6 - 22
4
,
CONNECTIONS
This is a
key step.(b)
Factor the numerator.= Divide out the common factor. NOW TRY
5 - 222
6
=
yA 5 - 222 B
6 y
= 28 y^2 = 24 y^2 # 2 = 2 y 22
5 y- 2 y 22
6 y
5 y- 28 y^2
6 y
, y 7 0
CAUTION Be careful to factor before writing a quotient in lowest terms.
NOW TRY ANSWERS
- (a) (b)
3 + 22
4
5 - 222
6