Name DateWORKSHEET 7.1: SIMPLIFYING RADICALS
-------------------------------------------------------------------------------------A radical is in simplest form if there are no perfect square factors other than 1 in the
radicand. Follow the steps below to simplify radicals:- Factor the radicand as a product of the largest perfect square and another number.
(The radicand is the number inside the radical symbol.) Examples of perfect squares
include 4, 9, 16, 25, 36, 49, 64, 81, 100,... - If you did not select the largest perfect square factor, determine if the other number
has a perfect square factor. If it does, factor the number. - Continue factoring until there are no numbers in the radicand that have a perfect
square (other than 1) as a factor. - Simplify your answer.
EXAMPLE
Simplify√
108. √
108 =
√
36 ·
√
3 = 6
√
3
or
√
108 =√
4 ·
√
27 =
√
4 ·
√
9 ·
√
3 = 2 · 3 ·
√
3 = 6
√
3
DIRECTIONS: Simplify each radical. If the radical cannot be simplified, write ‘‘cannot be
simplified.’’√
150 2.
√
63 3.
√
96 4.
√
200
√
76 6.
√
48 7.
√
55 8.
√
360
√
42 10.
√
54 11.
√
550 12.
√
252
CHALLENGE:Suresh simplified√
80 and said that it equals 2√- Is he
correct? Explain your answer.
253Copyright
©
2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.