PSAT Math : How to divide square roots

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Divide Square Roots

Divide and simplify. Assume all integers are positive real numbers. 

Possible Answers:

Correct answer:

Explanation:

 

There are two ways to solve this problem. First you can divide the numbers under the radical. Then simplify. 

Example 1

Example 2 

Find the square root of both numerator and denominator, simplifying as much as possible then dividing out like terms. 

Both methods will give you the correct answer of .

Example Question #1742 : Psat Mathematics

(√27 + √12) / √3 is equal to

Possible Answers:

√3

5

5/√3

18

(6√3)/√3

Correct answer:

5

Explanation:

√27 is the same as 3√3, while √12 is the same as 2√3.

3√3 + 2√3 = 5√3

(5√3)/(√3) = 5

Example Question #2 : How To Divide Square Roots

Simplify:

Possible Answers:

Correct answer:

Explanation:

To simplfy, we must first distribute the square root.

Next, we can simplify each of the square roots.

Example Question #3 : How To Divide Square Roots

Find the quotient:

Possible Answers:

Correct answer:

Explanation:

Find the quotient:

There are two ways to approach this problem.

Option 1: Combine the radicals first, the reduce

Option 2: Simplify the radicals first, then reduce

Example Question #4 : How To Divide Square Roots

Find the quotient:

Possible Answers:

Correct answer:

Explanation:

 

Simplify each radical:

 

Rationalize the denominator:

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