SAT Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for SAT Math

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Example Questions

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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+1

\frac{x}{10}

x^{2}

x^{4}

5x^{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.

Example Question #2 : Basic Squaring / Square Roots

Evaluate:

0.082

Possible Answers:

0.64

0.00064

0.0064

0.064

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

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 #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.

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:

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

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