Name DateWORKSHEET 7.4: DIVIDING RADICALS
-------------------------------------------------------------------------------------To divide radicals you must use the quotient property of square roots. This property states
that the square root of a quotient equals the quotient of the square roots.√
x
y=
√
x
√y, wherex
is a real number greater than or equal to 0 andyis a real number that is greater than 0.
Follow the steps below to divide radicals:- If one radical is a factor of the other, divide the radicals. If the radicals have a common
factor, simplify. - Simplify the radical expression.
- Radicands should have no common perfect square factor other than 1.
- No radicals should be in the denominator.
EXAMPLE
3√
12
√
10
Simplify the radicals because√
10 is not a factor of√
12.
3
√
12
√
10
= 3
√
12
10
= 3
√
6
5
=
3
√
6
√
5
Simplify the radical expression.3
√
6
√
5
·
√
5
√
5
=
3
√
30
√
25
=
3
√
30
5
DIRECTIONS: Simplify each expression.
√
3
√
15
√
14
√
20
4
√
6
√
2
√
20
√
5
3
√
6
√
8
√
27
√
30
√
15
√
3
√
40
√
12
CHALLENGE:Mary simplified√
64
16as√- Is she correct? If not, explain
why not.
259Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.