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SAT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

Example Question #1 : Basic Squaring / Square Roots

If all real values of $x$ lie between 0 and 1, which of the following is always greater than 1?

Possible Answers:

$x^{4}$

$x+1$

$5x^{2}$

$\frac{x}{10}$

$x^{2}$

Correct answer:

$x+1$

Explanation:

If $x$ is greater than 0, then adding 1 to $x$ will make it greater than 1. Taking a number between 0 and 1 to a power results in a smaller number.

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Example Question #2 : Basic Squaring / Square Roots

Evaluate:

0.08²

Possible Answers:

0.064

0.00064

0.64

0.0064

0.00064

Correct answer:

0.0064

Explanation:

0.08 * 0.08

First square 8:

8 * 8 = 64

Then move the decimal four places to the left:

0.0064

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Example Question #2 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\sqrt{.00081}=$

Possible Answers:

0.028

0.09

0.9

0.009

Correct answer:

0.028

Explanation:

The easiest way to find the square root of a fraction is to convert it into scientific notation.

$\dpi{100} \small .00081 = 8.1 \times 10^{-4}$

The key is that the exponent in scientific notation has to be even for a square root because the square root of an exponent is diving it by two. The square root of 9 is 3, so the square root of 8.1 is a little bit less than 3, around 2.8

$\dpi{100} \small \sqrt{8.1 \times 10^{-4}} \approx 2.8 \times 10^{-2} \approx 0.028$

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Example Question #7 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.0049}$

Possible Answers:

$\small 0.07$

$\small 0.022$

$\small 0.7$

$\small 0.007$

Correct answer:

$\small 0.07$

Explanation:

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

$\small 0.0049 = 49 \cdot10^{-4}$

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

$\small \sqrt{0.0049} = \sqrt{49}\cdot\sqrt{10^{-4}} = 7\cdot10^{-2} = 0.07$

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Example Question #8 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.025}$

Possible Answers:

$\small 0.005$

$\small 0.05$

$\small 0.158$

$\small 0.625$

Correct answer:

$\small 0.158$

Explanation:

This problem can be solve more easily by rewriting the decimal into scientific notation.

$\small 0.025 = 2.5 \times 10^{-2}$

Because $\small 10^{-2}$ has an even exponent, we can take the square root of it by dividing it by 2. The square root of 4 is 2, and the square root of 1 is 1, so the square root of 2.5 is less than 2 and greater than 1.

$\small \sqrt{0.025} = \sqrt{2.5}\times \sqrt{10^{-2}} = 1.58\times 10^{-1} = 0.158$

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Example Question #9 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.00036}$

Possible Answers:

$\small 0.006$

$\small 0.019$

$\small 0.013$

$\small 0.06$

Correct answer:

$\small 0.019$

Explanation:

This problem becomes much simpler if we rewrite the decimal in scientific notation

$\small 0.00036 = 3.6\times 10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can take its square root by dividing it by two. The square root of 4 is 2, and because 3.6 is a little smaller than 4, its square root is a little smaller than 2, around 1.9

$\small \sqrt{0.025} = \sqrt{3.6}\times \sqrt{10^{-4}} \approx 1.9\times 10^{-2} = 0.019$

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Example Question #21 : Decimals

Find the square root of the following decimal:

$\small \sqrt{0.00064}$

Possible Answers:

$\small 0.08$

$\small 0.0253$

$\small 0.008$

$\small 0.8$

Correct answer:

$\small 0.0253$

Explanation:

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

$\small \small 0.00064 = 6.4 \times10^{-4}$

Because $\small 10^{-4}$ has an even exponent, we can divide the exponenet by 2 to get its square root. The square root of 9 is 3, and the square root of 4 is two, so the square root of 6.4 is between 3 and 2, around 2.53

$\small \small \sqrt{0.00064} = \sqrt{6.4}\times\sqrt{10^{-4}} \approx 2.53 \times10^{-2} = 0.0253$

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Example Question #3 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.0169}$

Possible Answers:

$\small 0.0285$

$\small 0.0411$

$\small \small 0.0318$

$\small 0.13$

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 #11 : Basic Squaring / Square Roots

Find the square root of the following decimal:

$\small \sqrt{0.00001}$

Possible Answers:

$\small 0.00316$

$\small 0.01$

$\small 0.001$

$\small 0.0001$

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 #22 : Decimals

Find the square root of the following decimal:

$\small \sqrt{0.004}$

Possible Answers:

$\small 0.0632$

$\small 0.016$

$\small 0.002$

$\small 0.02$

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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SAT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for SAT Math

All SAT Math Resources

Example Questions

Example Question #1 : Basic Squaring / Square Roots

Example Question #2 : Basic Squaring / Square Roots

Example Question #2 : Basic Squaring / Square Roots

Example Question #7 : Basic Squaring / Square Roots

Example Question #8 : Basic Squaring / Square Roots

Example Question #9 : Basic Squaring / Square Roots

Example Question #21 : Decimals

Example Question #3 : Basic Squaring / Square Roots

Example Question #11 : Basic Squaring / Square Roots

Example Question #22 : Decimals

All SAT Math Resources

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