Teaching Notes 7.4: Dividing Radicals
To divide radicals, students must use the quotient property of square roots. As students apply
this property, they must be sure there is no radical in the denominator.- Explain that dividing radicals is similar to dividing integers. The quotient property of square
roots states that
√
x
y=
√
x
√ywherexis a real number greater than or equal to 0 andyis a real
number greater than 0. The quotient of two square roots is found by dividing the radicands.For example,√
30
√
2
=
√
30
2
=
√
15.
- Review the information and example on the worksheet with your students. Make sure that
your students understand the quotient property of square roots. Explain that a radical is in
simplest form when there are no perfect square factors other than 1 in the radicand and there
are no radicals in the denominator. If necessary, present this example:
√
2
10
=
√
1
5
=
√
1
√
5
=
1
√
5
. Emphasize that this expression must be simplified by rationalizing the denominator.
1
√
5=
1
√
5
·
√
5
√
5
=
√
5
√
25
=
√
5
5
You may find it helpful to review 7.3: ‘‘Rationalizing theDenominator.’’EXTRA HELP:
You can only divide one radicand by another radicand.ANSWER KEY:
(1)
√
5
5
(2)
√
70
10
(3) 4
√
3 (4) 2 (5)
3
√
3
2
(6)
3
√
10
10
(7)
√
5 (8)
√
30
3
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(Challenge)Her work is correct but she needs to continue to simplify√
4. The correct answer is 2.
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