How to multiply square roots

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SAT Math › How to multiply square roots

Questions 1 - 10

1

Simplify:

$-\sqrt{6}(\sqrt{5}-\sqrt{2})$

$2\sqrt{3}-\sqrt{30}$

$2\sqrt{3}+\sqrt{30}$

$3\sqrt{2}-\sqrt{30}$

$12-\sqrt{30}$

$-\sqrt{30}-2\sqrt{3}$

Explanation

To simplify the problem, just distribute the radical to each term in the parentheses.

$\-\sqrt{6}(\sqrt{5}-\sqrt{2})\=-\sqrt{30}+\sqrt{12}\=-\sqrt{30}+2\sqrt{3}$

2

Evaluate and simplify:

$\sqrt{10}*\sqrt{12}$

$2\sqrt{30}$

$\sqrt{22}$

$4\sqrt{5}$

$20\sqrt{6}$

$30\sqrt{2}$

Explanation

To multiply square roots, we multiply the numbers inside the radical and we can simplify them if possible.

$\ \sqrt{10}*\sqrt{12}\=\sqrt{10*12}\=\sqrt{120}\=\sqrt{4}*\sqrt{30}\=2\sqrt{30}$

3

Simplify: $\sqrt{7}*\sqrt{14}$

$7\sqrt{2}$

$\sqrt{98}$

$\sqrt{21}$

$7\sqrt{3}$

$2\sqrt{7}$

Explanation

When multiplying square roots, you are allowed to multiply the numbers inside the square root. Then simplify if necessary.

$\sqrt{7}*\sqrt{14}=\sqrt{7*14}=\sqrt{98}=\sqrt{49}*\sqrt{2}=7\sqrt{2}$

4

Simplify:

$4\sqrt{7}*\sqrt{21}$

$28\sqrt{3}$

$11\sqrt{3}$

$12\sqrt{21}$

$3\sqrt{7}$

$7\sqrt{7}$

Explanation

To multiply square roots, we multiply the numbers inside the radical.

Any numbers outside the radical are also multiplied.

We can simplify them if possible.

$\4\sqrt{7}*\sqrt{21}\ =4\sqrt{7*21}\=4\sqrt{7*7*3}\=4*7\sqrt{3}\=28\sqrt{3}$

5

Simplify:

$\sqrt{3}(\sqrt{3}+4)$

$3+4\sqrt{3}$

$7\sqrt{3}$

$3+2\sqrt{3}$

$9+4\sqrt{3}$

Explanation

To simplify the problem, just distribute the radical to each term in the parentheses.

$\\sqrt{3}(\sqrt{3}+4)\=\sqrt{9}+4\sqrt{3}\=3+4\sqrt{3}$

6

Simplify: $\sqrt{x+5}*\sqrt{x-5}$

$\sqrt{x^2-25}$

$\sqrt{x^2-10}$

Explanation

To multiply square roots, we multiply the numbers inside the radical and we can simplify them if possible.

$\\sqrt{x+5}*\sqrt{x-5}\=\sqrt{(x+5)(x-5)}\=\sqrt{x^2-25}$

7

Simplify: $\sqrt{24}*3\sqrt{8}$

$24\sqrt{3}$

$16\sqrt{6}$

$12\sqrt{3}$

$24\sqrt{6}$

$8\sqrt{14}$

Explanation

When multiplying square roots, you are allowed to multiply the numbers inside the square root. Then simplify if necessary.

$\sqrt{24}*3\sqrt{8}=3\sqrt{24*8}=3\sqrt{192}=3\sqrt{64}*\sqrt{3}=24\sqrt{3}$

8

Simplify:

$(\sqrt{2}+\sqrt{7})(\sqrt{27}+\sqrt{12})$

$5\sqrt{6}+5\sqrt{21}$

$3\sqrt{6}+2\sqrt{2}+2\sqrt{3}+3\sqrt{7}$

$3\sqrt{3}+2\sqrt{21}$

$2\sqrt{5}+5\sqrt{2}+3\sqrt{6}$

$5\sqrt{6}+2\sqrt{21}+3\sqrt{2}$

Explanation

$(\sqrt{2}+\sqrt{7})(\sqrt{27}+\sqrt{12})$

Let's simplify the right parentheses.

$(\sqrt{27}+\sqrt{12})=(3\sqrt{{3}}+2\sqrt{3})=5\sqrt{3}$

Now we can distribute the radical to each term in the parentheses.

$5\sqrt{3}(\sqrt{2}+\sqrt{7})=5\sqrt{6}+5\sqrt{21}$

9

Simplify:

$2\sqrt{10}*5\sqrt{20}$

$100\sqrt{2}$

$20\sqrt{5}$

$50\sqrt{2}$

$40\sqrt{10}$

Explanation

To multiply square roots, we multiply the numbers inside the radical.

Any numbers outside the radical are also multiplied.

We can simplify them if possible.

$\2\sqrt{10}*5\sqrt{20}\=10\sqrt{10*20}\=10\sqrt{10*10*2}\=10*10\sqrt{2}\=100\sqrt{2}$

10

Simplify:

$\sqrt{6}*2\sqrt{3}$

$6\sqrt{2}$

$6\sqrt{3}$

$2\sqrt{6}$

$4\sqrt{6}$

$12\sqrt{2}$

Explanation

To multiply square roots, we multiply the numbers inside the radical.

Any numbers outside the radical are also multiplied. We can simplify them if possible.

$\\sqrt{6}*2\sqrt{3}\=2\sqrt{6*3}\=2\sqrt{18}\=2\sqrt{9}*\sqrt{2}\=2*3\sqrt{2}\=6\sqrt{2}$

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