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 3√6 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.

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