PSAT Math : How to multiply square roots

Study concepts, example questions & explanations for PSAT Math

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Example Questions

Example Question #1 : How To Multiply Square Roots

Multiply and simplify. Assuming all integers are positive real numbers. 

Possible Answers:

Correct answer:

Explanation:

Multiply the coefficents outside of the radicals.

Then multiply the radicans. Simplify by checking for a perfect square. 

Final answer is your leading coefficent, , multiplied by the answer acquired by multiplying the terms under the radican,

The final answer is .

Example Question #1 : How To Multiply Square Roots

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

Possible Answers:

Correct answer:

Explanation:

Order of operations, first distributing the  to all terms inside the parentheses. 

The final answer is .

Example Question #1754 : Psat Mathematics

The square root(s) of 36 is/are ________.

Possible Answers:

-6

6, -6, and 0

6 and -6

6

None of these answers are correct.

Correct answer:

6 and -6

Explanation:

To square a number is to multiply that number by itself. Because 6 x 6 = 36 AND -6 x -6 = 36, both 6 and -6 are square roots of 36.

Example Question #3 : How To Multiply Square Roots

Simplify:

Possible Answers:

Correct answer:

Explanation:

Multiplication of square roots is easy! You just have to multiply their contents by each other. Just don't forget to put the result "under" a square root! Therefore:

becomes

Now, you need to simplify this:

You can "pull out" two s.  (Note, that it would be even easier to do this problem if you factor immediately instead of finding out that .)

After pulling out the s, you get:

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