Entire And Mixed Radicals Worksheet Page 2
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1
2
3
4Example 1: Simplify each radical (convert to mixed radical) by using prime factorization.
a) √ 63
b) √ 75
3
3
c) √ 120
d) √ 108
Converting Entire radicals to Mixed radicals, Using Perfect squares/cubes:
Recall the perfect squares and perfect cubes chart:
Consider: √ 32
We can look for a perfect square which is
Number
Square
Cube
a factor of 32 as follows:
1
1
1
√ ���� = √ 4 ⋅ 8
2
4
8
3
9
27
= √ 4 ⋅ √ 8
4
16
64
5
25
125
= 2 ⋅ √ 8
We can still find a perfect square in the
6
36
216
radicand, 8, so we still need to simplify:
7
49
343
= 2 ⋅ √ 4 ⋅ 2
8
64
512
9
81
729
= 2 ⋅ √ 4 ⋅ √ 2
10
100
1000
11
121
1331
= 2 ⋅ 2 ⋅ √ 2
12
144
1728
13
169
2197
= �� √ ��
14
196
2744
**Easier: find the
greatest perfect square
in 32
15
225
3375
√ ���� = √ 16 ⋅ 2
= √ 16 ⋅ √ 2
= �� √ ��
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