ACT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for ACT Math

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Example Questions

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Example Question #1 : How To Square A Decimal

Find the square of .

Possible Answers:

Correct answer:

Explanation:

Squaring a decimal is identical to multiplying decimals.

Drop the decimal, multiply the number by its self, and then add up the decimal points in the original problem and put it back into your answer.

 (note: 4 decimal places)

Example Question #2 : How To Square A Decimal

What is ?

Possible Answers:

Correct answer:

Explanation:

You can solve this on your calculator, or think about it as a fraction to make the problem easier to do by hand. .

Example Question #3 : How To Square A Decimal

If  and , what is  equal to?

Possible Answers:

Correct answer:

Explanation:

First, we must figure out what  is equal to.

We do .

Now to find out what  is equal to, we look at .

We move our decimal points over so that we are dealing with only whole numbers. This gives us .

Finally, we count how many spaces we moved our decimals in total, and we move the decimal in our answer back that many spaces. To get from  to  we moved our decimal two spaces to the right. Because we did this for each of the  values, our total spaces we moved the decimal was  to the right.

Therefore, we must take  and move the decimal  places to the left. This gives us .

Example Question #4 : How To Square A Decimal

Evaluate the following:

Possible Answers:

Correct answer:

Explanation:

To solve, simply multiply 0.02 by 0.02 as though the numbers are without decimals.

Then, sum the number of spaces to the right of the decimal points in your problem and include that many in your answer.

Thus, your answer is .0004.

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

Find the square root of the following decimal:

Possible Answers:

Correct answer:

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

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

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

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

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.

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

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

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

Because  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.

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

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

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

Because  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

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

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

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

Because  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

Example Question #6 : How To Find The Square Root Of A Decimal

Find the square root of the following decimal:

Possible Answers:

Correct answer:

Explanation:

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

Because  has an even exponent, we can divide the exponenet by 2 to get its square root.  is a perfect square, whose square root is .

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