GRE Math : Simplifying Square Roots

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Example Questions

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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Example Question #13 : Arithmetic

Reduce.

$\sqrt{368}$

Possible Answers:

$16\sqrt{23}$

$6\sqrt{2}$

$\sqrt{2}\sqrt{36}$

$2\sqrt{23}$

$4\sqrt{23}$

Correct answer:

$4\sqrt{23}$

Explanation:

To reduce this expression, first find factors of 368 , then reduce.

To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 368 and is also a perfect square.

The solution is:

$\sqrt{368}=\sqrt{16\times 23}=\sqrt{16}\sqrt{23}=4\sqrt{23}$

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Example Question #601 : Gre Quantitative Reasoning

Find the square root of 416 .

Possible Answers:

$4\sqrt{26}$

$4\sqrt{10}$

$8\sqrt{26}$

$4\sqrt{20}$

$4\sqrt{23}$

Correct answer:

$4\sqrt{26}$

Explanation:

To reduce this expression, first find factors of 416 , then reduce.

To simplify, we must try to find factors which are perfect squares. In this case 16 is a factor of 416 and is also a perfect square.

The solution is:

$\sqrt{416}=\sqrt{16\times 26}=\sqrt{16}\sqrt{26}=4\sqrt{26}$

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Example Question #1 : How To Simplify Square Roots

Simplify the following: (√(6) + √(3)) / √(3)

Possible Answers:

√(3)

None of the other answers

3√(2)

√(2) + 1

Correct answer:

√(2) + 1

Explanation:

Begin by multiplying top and bottom by √(3):

(√(18) + √(9)) / 3

Note the following:

√(9) = 3

√(18) = √(9 * 2) = √(9) * √(2) = 3 * √(2)

Therefore, the numerator is: 3 * √(2) + 3. Factor out the common 3: 3 * (√(2) + 1)

Rewrite the whole fraction:

(3 * (√(2) + 1)) / 3

Simplfy by dividing cancelling the 3 common to numerator and denominator: √(2) + 1

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Example Question #1 : How To Simplify Square Roots

what is

√0.0000490

Possible Answers:

0.00007

0.07

0.007

Correct answer:

0.007

Explanation:

easiest way to simplify: turn into scientific notation

√0.0000490= √4.9 X 10^-5

finding the square root of an even exponent is easy, and 49 is a perfect square, so we can write out an improper scientific notation:

√4.9 X 10^-5 = √49 X 10^-6

√49 = 7; √10^-6 = 10^-3 this is equivalent to raising 10^-6 to the 1/2 power, in which case all that needs to be done is multiply the two exponents: 7 X 10^-3= 0.007

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Example Question #5 : Simplifying Square Roots

Simplify: $\sqrt{576}$

Possible Answers:

$10\sqrt{12}$

$12\sqrt{3}$

$12\sqrt{6}$

Correct answer:

Explanation:

In order to take the square root, divide 576 by 2.

$\dpi{100} \sqrt{576}= \sqrt{2}\sqrt{288}=\sqrt{2}\sqrt{2}\sqrt{144}=\sqrt{4}\sqrt{144}=2\cdot 12=24$

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Example Question #601 : Gre Quantitative Reasoning

Simplify $(\frac{16}{81})^{1/4}$ .

Possible Answers:

$\frac{4}{81}$

$\frac{8}{81}$

$\frac{2}{81}$

$\frac{2}{3}$

$\frac{4}{9}$

Correct answer:

$\frac{2}{3}$

Explanation:

$(\frac{16}{81})^{1/4}$

$\frac{16^{1/4}}{81^{1/4}}$

$\frac{(2\cdot 2\cdot 2\cdot 2)^{1/4}}{(3\cdot 3\cdot 3\cdot 3)^{1/4}}$

$\frac{2}{3}$

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Example Question #5 : How To Simplify Square Roots

Simplfy the following radical $\sqrt{20x^{2}}$ .

Possible Answers:

$2\sqrt{5x^{2}}$

$4\sqrt{5x}$

$2x\sqrt{10}$

$2x\sqrt{5}$

Correct answer:

$2x\sqrt{5}$

Explanation:

You can rewrite the equation as $\sqrt{20x^2}=(x)\sqrt{5} \cdot \sqrt{4}$ .

This simplifies to $2x\sqrt{5}$ .

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Example Question #602 : Gre Quantitative Reasoning

Which of the following is equal to $\sqrt{75}$ ?

Possible Answers:

$3\sqrt{5}$

$7.5\sqrt{10}$

$5\sqrt{3}$

Correct answer:

$5\sqrt{3}$

Explanation:

√75 can be broken down to √25 * √3. Which simplifies to 5√3.

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GRE Math : Simplifying Square Roots

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

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

Example Question #11 : Arithmetic

Example Question #13 : Arithmetic

Example Question #601 : Gre Quantitative Reasoning

Example Question #1 : How To Simplify Square Roots

Example Question #1 : How To Simplify Square Roots

Example Question #5 : Simplifying Square Roots

Example Question #601 : Gre Quantitative Reasoning

Example Question #5 : How To Simplify Square Roots

Example Question #602 : Gre Quantitative Reasoning

All GRE Math Resources

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