# Square Roots - How to Simplify Square Roots - Part 2

## How to Simplify Square Roots - How it Works - Video

### Example 1 Example 1:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 20 as a factor pair where one number is a square number so we can cancel the inverses. We have the options to rewrite 20 as 1*20 or 2*10 or 4*5. Only, one has a square number greater than one ==> 4*5.

√20

• √4*5 We rewrite as a multiplication of two numbers.

• √4*√5 We separate the two numbers as two square roots.

• √22 *√5 We rewrite 4 as a numbered squared.

• 2√5 The inverses (squares and square roots) cancel.

So 2√5 is the final answer.

### Example 2 Example 2:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 71 as a factor pair where one number is a square number so we can cancel the inverses. We only have the options to rewrite 20 as 1*71. So that means 71 is a prime number and we can't simplify.

√71

• √71*1 We rewrite as a multiplication of two numbers.

• √71 71 is a prime number.

So √71 is our final answer.

### Example 3 Example 3:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 54 as a factor pair where one number is a square number so we can cancel the inverses. We have the options to rewrite 54 as 1*54 or 2*27 or 3*18 or 6*9. Only, one has a square number greater than one ==> 6*9.

-54

• -1*9*6 We rewrite as a multiplication of two numbers.

• -1*9*√6 We separate the two numbers as two square roots.

• -1*32 *√6 We rewrite 4 as a numbered squared.

• -1*3*6 The inverses (squares and square roots) cancel.

• -3√6 We multiply -1 and 3.

We can't simplify √6 because 6 can only be written 1*6 or 2*3. There aren't any square numbers greater than 1. So 36 is the final answer.

### Example 4 Example 4:

When simplifying square roots or radicals, we need to look for square numbers, since squares are the inverse of square roots. We need to rewrite 30 as a factor pair where one number is a square number so we can cancel the inverses. We have the options to rewrite 30 as 1*30 or 2*15 or 3*10 or 5*6. None of those factor pairs are greater than one so we can't simplify anymore.

30

• 30 We can't simplify any further.

So √30 is the final answer.

## Live Worksheet

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