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SAT Math : Square Roots and Operations

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Example Questions

Example Question #1 : How To Multiply Square Roots

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

Possible Answers:

$\sqrt{21}$

$7\sqrt{3}$

$2\sqrt{7}$

$\sqrt{98}$

$7\sqrt{2}$

Correct answer:

$7\sqrt{2}$

Explanation:

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

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

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Example Question #1 : Basic Squaring / Square Roots

Simplify: $\sqrt{10}*\sqrt{15}$

Possible Answers:

$\sqrt{150}$

$10\sqrt{2}$

$6\sqrt{5}$

$75\sqrt{2}$

$5\sqrt{6}$

Correct answer:

$5\sqrt{6}$

Explanation:

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

$\sqrt{10}*\sqrt{15}=\sqrt{10*15}=\sqrt{150}=\sqrt{25}*\sqrt{6}=5\sqrt{6}$

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Example Question #1 : Basic Squaring / Square Roots

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

Possible Answers:

$8\sqrt{14}$

$16\sqrt{6}$

$24\sqrt{6}$

$24\sqrt{3}$

$12\sqrt{3}$

Correct answer:

$24\sqrt{3}$

Explanation:

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

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

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Example Question #1 : How To Multiply Square Roots

Simplify:

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

Possible Answers:

$\sqrt{18}+\sqrt{10}$

$\sqrt{6}+\sqrt{18}+\sqrt{10}+\sqrt{30}+8$

$4\sqrt{6}+5\sqrt{2}+\sqrt{3}$

$\sqrt{6}+3\sqrt{2}+\sqrt{10}+\sqrt{30}$

$\sqrt{6}+\sqrt{30}$

Correct answer:

$\sqrt{6}+3\sqrt{2}+\sqrt{10}+\sqrt{30}$

Explanation:

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

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

$\sqrt{6}+\sqrt{18}+\sqrt{10}+\sqrt{30}=$

$\sqrt{6}+3\sqrt{2}+\sqrt{10}+\sqrt{30}$

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Example Question #2 : How To Multiply Square Roots

Evaluate and simplify:

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

Possible Answers:

$\sqrt{22}$

$2\sqrt{30}$

$4\sqrt{5}$

$30\sqrt{2}$

$20\sqrt{6}$

Correct answer:

$2\sqrt{30}$

Explanation:

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

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

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Example Question #1 : How To Multiply Square Roots

Simplify and evaluate:

$\sqrt{12}*\sqrt{48}$

Possible Answers:

$8\sqrt{3}$

$24\sqrt{3}$

$16\sqrt{2}$

Correct answer:

Explanation:

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

In this case, let's simplify each individual radical and multiply them.

$\\\sqrt{12}*\sqrt{48}\\=\sqrt{4}*\sqrt{3}*\sqrt{16}*\sqrt{3}\\=2\sqrt{3}*4\sqrt{3}\\=8*3=24$

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Example Question #1 : How To Multiply Square Roots

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

Possible Answers:

$\sqrt{x^2-25}$

x-5

x+5

$\sqrt{x^2-10}$

x^2-25

Correct answer:

$\sqrt{x^2-25}$

Explanation:

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

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

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Example Question #1 : How To Multiply Square Roots

Simplify:

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

Possible Answers:

$2\sqrt{6}$

$6\sqrt{3}$

$12\sqrt{2}$

$4\sqrt{6}$

$6\sqrt{2}$

Correct answer:

$6\sqrt{2}$

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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Example Question #1 : Square Roots And Operations

Simplify:

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

Possible Answers:

$11\sqrt{3}$

$7\sqrt{7}$

$12\sqrt{21}$

$3\sqrt{7}$

$28\sqrt{3}$

Correct answer:

$28\sqrt{3}$

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.

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

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Example Question #1 : How To Multiply Square Roots

Simplify:

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

Possible Answers:

$50\sqrt{2}$

200

$100\sqrt{2}$

$40\sqrt{10}$

$20\sqrt{5}$

Correct answer:

$100\sqrt{2}$

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.

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

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SAT Math : Square Roots and Operations

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : How To Multiply Square Roots

Example Question #1 : Basic Squaring / Square Roots

Example Question #1 : Basic Squaring / Square Roots

Example Question #1 : How To Multiply Square Roots

Example Question #2 : How To Multiply Square Roots

Example Question #1 : How To Multiply Square Roots

Example Question #1 : How To Multiply Square Roots

Example Question #1 : How To Multiply Square Roots

Example Question #1 : Square Roots And Operations

Example Question #1 : How To Multiply Square Roots

All SAT Math Resources

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