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ACT Math : Basic Squaring / Square Roots

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Example Questions

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

Find the square root of the following decimal:

$\small \sqrt{0.00001}$

Possible Answers:

$\small 0.0001$

$\small 0.001$

$\small 0.01$

$\small 0.00316$

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 #5 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

$\small \sqrt{0.004}$

Possible Answers:

$\small 0.002$

$\small 0.016$

$\small 0.02$

$\small 0.0632$

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 #1 : How To Find The Square Root Of A Decimal

Find the square root of 0.16 .

Possible Answers:

0.004

0.0256

0.04

0.4

0.256

Correct answer:

0.4

Explanation:

Rewrite the expression in radical form.

$\sqrt{0.16}$

Rewrite the decimal with factors and simplify.

$\sqrt{0.16} = \sqrt{0.4\cdot 0.4} = \sqrt{0.4}\cdot \sqrt{0.4}=0.4$

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Example Question #1 : How To Find The Square Root Of A Decimal

Find the square root of 0.04 .

Possible Answers:

0.2

0.0016

0.002

0.0002

0.02

Correct answer:

0.2

Explanation:

Rewrite the question in radical form.

$\sqrt{0.04}$

Split up 0.04 into its common factor.

$\sqrt{0.2 \cdot 0.2} = \sqrt{0.2} \cdot \sqrt{0.2} = 0.2$

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Example Question #281 : Arithmetic

Evaluate: $-\sqrt{0.0001}$

Possible Answers:

-0.1

-0.01

-1.01

-0.0001

$Answer \:does \:not\ exist.$

Correct answer:

-0.01

Explanation:

The answer exists because the number inside the radical is not negative.

First evaluate $\sqrt{0.0001}$ by splitting the inside number by its common factor.

$\sqrt{0.0001}= \sqrt{0.01 \cdot 0.01} = 0.01$

The negative sign before the radical means that the negative is distributed after evaluating the radical.

$-(\sqrt{0.0001})= -(0.01)= -0.01$

Therefore, the answer is -0.01 .

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Example Question #282 : Arithmetic

Evaluate: $\sqrt{-0.64}$

Possible Answers:

-0.4096

-0.04096

-0.8

-0.008

$Answer\: does\: not\: exist.$

Correct answer:

$Answer\: does\: not\: exist.$

Explanation:

The answer does not exist since it's not possible to take the square root of negative numbers.

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Example Question #972 : Gre Quantitative Reasoning

Solve for :

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

Possible Answers:

0.2

0.64

0.08

0.4

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 #391 : Arithmetic

Find the square root of the following decimal:

$\small \sqrt{0.00000025}$

Possible Answers:

$\small 0.005$

$\small 0.00025$

0.00158

$\small 0.0005$

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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Example Question #1357 : Act Math

If $x=\sqrt{\frac{1}{0.25}}$ , which of the following is true?

Possible Answers:

x<1

2>x>1

1<x<3

0<x<1

x=1

Correct answer:

1<x<3

Explanation:

$\sqrt{\frac{1}{0.25}}=\frac{\sqrt{1}}{\sqrt{0.25}}=\frac{1}{0.5}=2$

To convince yourself that 0.5 is indeed the square root of 0.25 , let's square 0.5 .

$0.5\times0.5=0.25$ , so this is true. Since we now know that x=2 , the answer that is true given this information is 1<x=2<3 .

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ACT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for ACT Math

All ACT Math Resources

Example Questions

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

Example Question #5 : How To Find The Square Root Of A Decimal

Example Question #1 : How To Find The Square Root Of A Decimal

Example Question #1 : How To Find The Square Root Of A Decimal

Example Question #281 : Arithmetic

Example Question #282 : Arithmetic

Example Question #972 : Gre Quantitative Reasoning

Example Question #391 : Arithmetic

Example Question #1357 : Act Math

All ACT Math Resources

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