SAT Math : How to simplify square roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

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Example Question #51 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To eliminate a radical expression, we need to multiply top and bottom by the denominator.

Then simplify if necessary.

Example Question #151 : Arithmetic

If , simplify 

Possible Answers:

Correct answer:

Explanation:

In order to simplify the expression, we must see if we can factor out any perfect squares. 

In this case, we can factor out 16x2.

Because of the rules of square roots, this can be rewritten as:

Because  simplifies to 

Thus, we can rewrite as 

 

Example Question #51 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify square roots, factor the inside completely to find perfect squares:

Then separate into several roots being multiplied:

Simplify:

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