GRE Math : GRE Quantitative Reasoning

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Example Questions

Example Question #1 : Simplifying Square Roots

Simplify.

$\sqrt{624}$

Possible Answers:

$16\sqrt{39}$

$\sqrt{39}$

$8\sqrt{39}$

$2\sqrt{39}$

$4\sqrt{39}$

Correct answer:

$4\sqrt{39}$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 624 and is also a perfect square.

Therefore we can rewrite the square root of 624 as:

$\sqrt{624}=\sqrt{16\times 39}=\sqrt{16}\sqrt{39}=4\sqrt{39}$

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Example Question #1 : How To Find The Common Factors Of Squares

Reduce $\sqrt{400}$ to its simplest form.

Possible Answers:

$4\sqrt2$

$\sqrt{20}$

$\sqrt{200}$

$2\sqrt{20}$

Correct answer:

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 20 is a factor of 400 and is also a perfect square.

Thus we can rewrite the problem as:

$\sqrt{400}=\sqrt{20\times 20}=20$

Note: $20^{2}=20\times20=400$

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Example Question #4 : Arithmetic

Simplify.

$\sqrt{720}$

Possible Answers:

$12\sqrt{5}$

$5\sqrt{144}$

$\sqrt{12}$

$\sqrt{720}$

$144\sqrt{5}$

Correct answer:

$12\sqrt{5}$

Explanation:

Use the following steps to reduce this square root.

To simplify, we must try to find factors which are perfect squares. In this case 144 is a factor of 720 and is also a perfect square.

Thus we can rewrite the problem as follows.

$\sqrt{720}=\sqrt{144\times 5}=\sqrt{144}\sqrt{5}=12\sqrt{5}$

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Example Question #1 : Simplifying Square Roots

Find the square root of 1,800 .

Possible Answers:

$\sqrt{32}$

$30\sqrt{2}$

$2\sqrt{60}$

900

Correct answer:

$30\sqrt{2}$

Explanation:

Use the following steps to find the square root of 1,800:

To simplify, we must try to find factors which are perfect squares. In this case 900 is a factor of 1800 and is also a perfect square.

Thus we can rewrite the problem as follows.

$\sqrt{1,800}=\sqrt{900\times 2}=\sqrt{900}\sqrt{2}=30\sqrt{2}$

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Example Question #2 : Basic Squaring / Square Roots

Simplify.

$\sqrt{54}$

Possible Answers:

$6\sqrt{6}$

$3\sqrt{6}$

$9\sqrt{6}$

$\sqrt{3}$

$2\sqrt{6}$

Correct answer:

$3\sqrt{6}$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 9 is a factor of 54 and is also a perfect square.

To reduce this expression, use the following steps:

$\sqrt{54}=\sqrt{9\times 6}=\sqrt{9}\sqrt{6}=3\sqrt{6}$

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Example Question #1 : Simplifying Square Roots

Reduce.

$\sqrt{72}$

Possible Answers:

$2\sqrt{21}$

$4\sqrt{36}$

$36\sqrt{2}$

$2\sqrt{6}$

$6\sqrt{2}$

Correct answer:

$6\sqrt{2}$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 36 is a factor of 72 and is also a perfect square.

To reduce this expression, use the following arithmetic steps:

$\sqrt{72}=\sqrt{36\times 2}=\sqrt{36}\sqrt{2}=6\sqrt{2}$

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Example Question #1 : How To Find The Common Factors Of Squares

Which quantity is greater: $\sqrt{900}$ or ?

Possible Answers:

$30>\sqrt{900}$

$\sqrt{900}=\pm30$

Not enough information to determine the relationship between these two quantities.

$\sqrt{900}=30$

$30<\sqrt{900}$

Correct answer:

$\sqrt{900}=\pm30$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 30 is a factor of 900 and is also a perfect square.

The square root of 900 is equal to:

$\sqrt{900}=\sqrt{30\times 30}=30$

However,

$\sqrt{900}=\sqrt{-30\times -30}=-30$

Thus, $\pm30$ $=\sqrt{900}$

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Example Question #2 : Simplifying Square Roots

Reduce.

$\sqrt{32}$

Possible Answers:

$2\sqrt{2}$

$4\sqrt{2}$

$8\sqrt{2}$

$\sqrt{4}$

$16\sqrt{2}$

Correct answer:

$4\sqrt{2}$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 32 and is also a perfect square.

To reduce this expression, use the following steps:

$\sqrt{32}=\sqrt{16\times 2}=\sqrt{16}\sqrt{2}=4\sqrt{2}$

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Example Question #11 : How To Find The Common Factors Of Squares

Find the square root of 164 .

Possible Answers:

$2\sqrt{41}$

$2\sqrt{43}$

$\sqrt{43}$

$8\sqrt{2}$

$4\sqrt{41}$

Correct answer:

$2\sqrt{41}$

Explanation:

To simplify, we must try to find factors which are perfect squares. In this case 4 is a factor of 164 and is also a perfect square.

To find the square root of 164 , use the following steps:

$\sqrt{164}=\sqrt{4\times 41}=\sqrt{41}\sqrt{4}=2\sqrt{41}$

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Example Question #11 : Arithmetic

Reduce.

$\sqrt{192}$

Possible Answers:

$8\sqrt{3}$

$3\sqrt{4}$

$64\sqrt{3}$

$4\sqrt{3}$

$64\sqrt{4}$

Correct answer:

$8\sqrt{3}$

Explanation:

Use the following arithmetic steps to reduce $\sqrt{192}$ .

To simplify, we must try to find factors which are perfect squares. In this case 64 is a factor of 192 and is also a perfect square.

Note and are both factors of 192 , however only $\sqrt{64}$ can be reduced.

$\sqrt{192}=\sqrt{64\times 3}=\sqrt{64}\sqrt{3}=8\sqrt{3}$

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GRE Math : GRE Quantitative Reasoning

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #1 : Simplifying Square Roots

Example Question #1 : How To Find The Common Factors Of Squares

Example Question #4 : Arithmetic

Example Question #1 : Simplifying Square Roots

Example Question #2 : Basic Squaring / Square Roots

Example Question #1 : Simplifying Square Roots

Example Question #1 : How To Find The Common Factors Of Squares

Example Question #2 : Simplifying Square Roots

Example Question #11 : How To Find The Common Factors Of Squares

Example Question #11 : Arithmetic

All GRE Math Resources

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