(b)
(c)
Less work is involved if we simplify the radical in the denominator first.
Now we rationalize the denominator.
NOW TRYRationalizing Denominators in Roots of FractionsSimplify each radical. In part (b),
(a)
Quotient ruleFactor.Product ruleMultiply by.Product rule=- Multiply.
3210
25
=-
3210
5 # 5
25
25=-
322 # 25
525 # 25=-
322
525
=-
29 # 2
225 # 5=-
218
2125
-
B
18
125
p 7 0.
EXAMPLE 3
- 3
23
=
- 3 # 23
23 # 23
=
- 323
3
=- 23
- 6
212
=
- 6
24 # 3
=
- 6
223
=
- 3
23
- 6
212
522
25
=
522 # 25
25 # 25=
5210
5
= 210
460 CHAPTER 8 Roots, Radicals, and Root Functions
NOW TRY
EXERCISE 2
Rationalize each denominator.
(a) (b)
(c)
- 10
220
927
23
8
213
NOW TRY
EXERCISE 3
Simplify each radical.
(a)
(b)
B
48 x^8
y^3, y 70-
B
27
80 (b)
Quotient ruleProduct ruleMultiply by.Product ruleMultiply.NOW TRY=
5 m^222 p
p^3
=
5 m^222 p
p^2 #p
2 p
2 p=
5 m^222 # 2 p
p^22 p# 2 p=
5 m^222
p^22 p
=
250 m^4
2 p^5
B
50 m^4
p^5
Rationalizing Denominators with Cube and Fourth RootsSimplify.
(a)
Use the quotient rule, and simplify the numerator and denominator.
Since 2 # 4 = 8,a perfect cube, multiply the numerator and denominator by 234.
B
3
27
16
=
2327
2316
=
3
238 # 232
=
3
2232
B
3
27
16
EXAMPLE 4
NOW TRY ANSWERS
- (a) (b)
(c)- (a) (b)
4 x^423 y
y^2- 3215
20 - 25
3221
8213
13