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SAT Math : How to multiply square roots

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Example Questions

Example Question #11 : How To Multiply Square Roots

Simplify:

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

Possible Answers:

$9+4\sqrt{3}$

$3+2\sqrt{3}$

$3+4\sqrt{3}$

$7\sqrt{3}$

Correct answer:

$3+4\sqrt{3}$

Explanation:

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

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

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Example Question #82 : Arithmetic

Simplify:

$\sqrt{3}(\sqrt{7}+\sqrt{12})$

Possible Answers:

$\sqrt{21}+6$

$21+3\sqrt{3}$

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

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

$12+4\sqrt{3}$

Correct answer:

$\sqrt{21}+6$

Explanation:

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

$\\\sqrt{3}(\sqrt{7}+\sqrt{12})\\=\sqrt{21}+\sqrt{36}\\=\sqrt{21}+6$

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Example Question #83 : Arithmetic

Simplify:

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

Possible Answers:

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

$12-\sqrt{30}$

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

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

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

Correct answer:

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

Explanation:

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

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

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Example Question #21 : Basic Squaring / Square Roots

Simplify:

$-2\sqrt{5}(7\sqrt{3}+3\sqrt{10})$

Possible Answers:

$-19\sqrt{10}$

$-14\sqrt{15}-30\sqrt{2}$

$-14\sqrt{5}+30\sqrt{2}$

$-14\sqrt{5}-5\sqrt{2}$

$14\sqrt{5}-6\sqrt{2}$

Correct answer:

$-14\sqrt{15}-30\sqrt{2}$

Explanation:

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

$\\-2\sqrt{5}(7\sqrt{3}+3\sqrt{10})\\=-14\sqrt{15}-6\sqrt{50}$

$\\-14\sqrt{15}-6\sqrt{50}\\=-14\sqrt{15}-6*5\sqrt{2}\\=-14\sqrt{15}-30\sqrt{2}$

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Example Question #21 : Basic Squaring / Square Roots

Simplify:

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

Possible Answers:

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

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

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

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

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

Correct answer:

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

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.

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

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SAT Math : How to multiply square roots

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #11 : How To Multiply Square Roots

Example Question #82 : Arithmetic

Example Question #83 : Arithmetic

Example Question #21 : Basic Squaring / Square Roots

Example Question #21 : Basic Squaring / Square Roots

All SAT Math Resources

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