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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."