GRE Math : How to find the square root of a decimal

Study concepts, example questions & explanations for GRE Math

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Example Questions

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 #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. 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 #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.  is a perfect square, whose square root is .

Example Question #11 : Basic Squaring / Square Roots

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, so the square root of 10 should be a little larger than 3, around 3.16

Example Question #1351 : Act Math

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 36 is 6, so the square root of 40 should be a little more than 6, around 6.32. 

Example Question #1353 : Act Math

Solve for :

Possible Answers:

Correct answer:

Explanation:

Just like any other equation, isolate your variable. Start by multiplying both sides by :

Now, this is the same as:

You know that  is . You can intelligently rewrite this problem as:

, which is the same as:

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:

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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