SAT Math : How to simplify square roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #41 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify square roots, we need to factor out perfect squares. In this case, it's .

Example Question #42 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the radical, we should factor out perfect squares. 

Example Question #43 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the square roots, we need to factor out the perfect squares.

Example Question #141 : Arithmetic

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the square roots, we need to factor out perfect squares. 

We can combine to have two different bases. Remember .

Example Question #41 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the square root, we need to determine the value of the exponent and then simplify the radical.

 Now let's find perfect squares.

Example Question #46 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the square root, we need to determine the value of the exponent and then simplify the radical.

 Now let's find perfect squares.

Example Question #47 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the radical, we need to find perfect squares. Then if possible, we can reduc the fraction.

Example Question #41 : How To Simplify Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify the radical, let's deal with the parentheses first and apply the exponents. Reduce if necessary.

Example Question #49 : 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 conjugate which is opposite the sign in the expression. Then simplify if necessary.

Example Question #81 : Basic Squaring / Square Roots

Simplify: 

Possible Answers:

Correct answer:

Explanation:

To simplify square roots, we need to find perfect squares to factor out.

 

We can also simplify

Thus,

We can compute the numbers outside to get a final answer of .

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