Teaching Notes 7.2: Multiplying Radicals
To multiply radicals, students must use the product property of square roots. This property not
only allows students to multiply radicals, but it also allows them to simplify radicals.- Explain that multiplying radicals is similar to multiplying integers. The product property
of square roots states that
√
xy=√
x·√
y,wherexandyare real numbers that are greater
than or equal to 0. The product of two square roots is found by multiplying the radicands. For
example,√
5 ·
√
10 =
√
50.
- Explain that an answer is in simplest form when there are no perfect square factors other
than 1 in the radicand. Ask your students if
√
50 is in simplest form. The answer, of
course, is no.- Review how to simplify radicals by presenting this example: Simplify
√
50 by writing√
50
as the product of√
25 and√
- Because
√
25 =5,
√
50 expressed in simplest form is 5√
2.
Depending on the abilities of your students, you may wish to review 7.1: ‘‘Simplifying
Radicals.’’- Review the information and the example on the worksheet with your students. Note that it is
best to multiply the coefficients last.
EXTRA HELP:
Knowing your multiplication facts is aprerequisite skill for multiplying radicals.ANSWER KEY:
(1) 2√
5 (2) 2
√
14 (3) 18
√
2 (4) 3
√
5 (5) 2
√
35 (6) 9
√
6 (7)− 4
√
15 (8)− 20
√
5
------------------------------------------------------------------------------------------
(9)− 60
√
6 (10) 24 (11) 3
√
30 (12)− 32
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(Challenge)His method will work; however, Bobby needs to simplify his product, 2√
12, as 4√
3,
------------------------------------------------------------------------------------------which is the correct answer.254 THE ALGEBRA TEACHER’S GUIDE