GRE Math : Basic Squaring / Square Roots

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Example Questions

Example Question #384 : Arithmetic

Find the square root of the following decimal:

$\small \sqrt{0.0169}$

Possible Answers:

$\small 0.0411$

$\small 0.13$

$\small \small 0.0318$

$\small 0.0285$

Correct answer:

$\small 0.13$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.0169 = 169\times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 169$ is a perfect square, whose square root is $\small 13$ .

$\small \small \sqrt{0.0169} = \sqrt{169}\times \sqrt{10^{-4}} =13\times10^{-2} = 0.13$

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Example Question #2 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.00001}$

Possible Answers:

$\small 0.0001$

$\small 0.01$

$\small 0.001$

$\small 0.00316$

Correct answer:

$\small 0.00316$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small \small 0.00001 = 10 \times10^{-6}$

Because $\small \small 10^{-6}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, so the square root of 10 should be a little larger than 3, around 3.16

$\small \small \sqrt{0.00001} = \sqrt{10}\times \sqrt{10^{-6}} = 3.16\times10^{-3} = 0.00316$

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Example Question #4 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.004}$

Possible Answers:

$\small 0.016$

$\small 0.02$

$\small 0.002$

$\small 0.0632$

Correct answer:

$\small 0.0632$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.004 = 40 \times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 36 is 6, so the square root of 40 should be a little more than 6, around 6.32.

$\small \small \small \sqrt{0.004} = \sqrt{40}\times\sqrt{10^{-4}} \approx 6.32 \times10^{-2} = 0.0632$

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Example Question #3 : How To Find The Square Root Of A Decimal

Solve for :

$\frac{x}{\sqrt{0.04}}=\sqrt{0.16}$

Possible Answers:

0.08

0.4

0.64

0.2

Correct answer:

0.08

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by $\sqrt{0.04}$ :

$x=\sqrt{0.16}*\sqrt{0.04}$

Now, this is the same as:

$x=\sqrt{0.0064}$

You know that $\sqrt{64}$ is . You can intelligently rewrite this problem as:

$x=\sqrt{0.0064}=\sqrt{\frac{1}{10\textup{,}000}*64}$ , which is the same as:

$\sqrt{\frac{1}{10\textup{,}000}*64}=\sqrt{\frac{1}{10\textup{,}000}}*\sqrt{64}=\frac{1}{100}*8=0.08$

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Example Question #8 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.00000025}$

Possible Answers:

$\small 0.00025$

0.00158

$\small 0.0005$

$\small 0.005$

Correct answer:

$\small 0.0005$

Explanation:

To find the square root of this decimal we convert it into scientific notation.

$\small \small 0.00000025 = 25 \times 10^{-8}$

Because $\small \small 10^{-8}$ has an even exponent, we can divide the exponenet by 2 to get its square root. $\small 25$ is a perfect square, whose square root is $\small 5$ .

$\small \small \sqrt{0.00000025} = \sqrt{25}\times \sqrt{10^{-8}} = 5\times10^{-4} = 0.0005$

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GRE Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for GRE Math

All GRE Math Resources

Example Questions

Example Question #384 : Arithmetic

Example Question #2 : How To Find The Square Root Of A Decimal

Example Question #4 : How To Find The Square Root Of A Decimal

Example Question #3 : How To Find The Square Root Of A Decimal

Example Question #8 : How To Find The Square Root Of A Decimal

All GRE Math Resources

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