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Simplifying Radicals

by Melissa Pemberton

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Simplifying Radicals
Activity # 1 - Perfect Squares
Match the perfect squares with the integers we multiply to get them.
Expressions
Perfect Squares
2 x 2
36
5 x 5
1
8 x 8
16
10 x 10
49
9 x 9
4
7 x 7
100
1 x 1
64
4 x 4
25
6 x 6
81
3 x 3
9
Activity # 2 - Label the Parts
Look at the image below. Drag and drop the vocabulary words to label the different parts of the expression.
Index
Radicand
Radical/root
Coefficient
Activity # 3 - Matching Square Roots to Solutions
√1
2
√25
5
√4
7
√64
10
√16
3
√81
6
√36
8
√9
1
√100
9
√49
4
The Five Step Solution to Simplifying Radicals
Example # 1: √32
Step 1: Find the largest perfect square
1 x 32
2 x 16
4 x 8
The perfect squares are circled here. The largest of these is 16 so we'll use 2 x 16!
Step 2: Put the products under radicals
√(2 x 16)
Step 3: Give each product its own radical
√2 x √16
We know 16 is a perfect square, so we can take the square root of 16 and get 4 (because 4 x 4 = 16).
Step 4: Simplify perfect squares
√2 x 4
Step 5: Multiply
4√2
Put the 4 in front as the coefficient
The Five Step Solution with Variables
Example # 1: √(180n^4)
Step 1: Find the largest perfect square
2 x 90
5 x 36
Step 2: Put the products under radicals
√(5 x 36 x n^4)
We can think of "n^4" as "n x n x n x n."
Step 3: Give each product its own radical
√5 x √36 x √(n^4)
Step 4: Simplify perfect squares
√5 x 6 x n x n
Step 5: Multiply
6n^2√5
We know we need a pair of the same number to get a perfect square. We have two pairs here that we can pull out, so we are left with "n x n."
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