Download 10.4 Dividing Radical Expressions

10.4 Dividing Radical Expressions
Math 51
Professor Busken
Objectives
• Divide and simplify Radical Expressions
• Rationalize denominators or numerators that have one term
Exercises
1.
Simplify by taking roots of the numerator and denominator. Assume all variables represent positive
numbers.
s
r
r
r
4 6
4
49
12x5
3 27x y
4 32x
a)
b)
c)
d)
100
49x
8x
2y4 z8
2.
Divide and simplify, if possible. Assume all variables represent positive real numbers.
p
√
√
50x
48x
56xy3
√
a) √
b) √
c)
3x
2x
7x
p
p
√
3
5
3
189x5 y7
x
x2 y4
p
p
√
e)
d)
f)
4
3
8
x
7x2 y2
xy3
3.
Rationalize each denominator. Assume all variables represent positive numbers.
r
√
√
√
3
2
3 6
5x
3
√
√
a)
b)
d)
c) √
3
7
10y
4 2
5
4.
e)
Rationalize each numerator. Assume all variables represent positive numbers.
r
r
√
√
5
3 5
4x
3 7
√
a)
b)
c)
d)
3
8
7
5 2
Answers: 1a) 7/10
p
2d) 3xy 3 y2
2e)
√
3
6x2 y
3e)
4a)
3y
1b)
√
12
x
√5
15
√
2x2 3
7
2f)
4b)
√
3
1c)
3xy2
2
10x2 y2
2y
√3
10
1d)
3a)
4c)
2
√
14
7
7
√
3
49
2x
yz2
2a)
3b)
4d)
√
3 3
4
2x
√
7 x
e)
5
2b)
4
√
2xy
2y
3c)
4e)
z
2x
√
3
2x2 z
√
3
2x2
p
3
9y2
√
3
4x
√
3 4
z
2c)
3d)
√
2y 2y
√
3
75
5