How to multiply square roots

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PSAT Math › How to multiply square roots

Questions 1 - 4
1

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

6 and -6

6

-6

6, -6, and 0

None of these answers are correct.

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.

2

Simplify:

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:

3

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

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 .

4

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

Explanation

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

The final answer is .

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