GRE Math : Basic Squaring / Square Roots

Study concepts, example questions & explanations for GRE Math

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Example Questions

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Example Question #1 : Basic Squaring / Square Roots

Which quantity is greater? When 

Quantity A  

 

Quantity B 

1

Possible Answers:

The two quantities are equal.

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

Correct answer:

Quantity B is greater.

Explanation:

X must equal a number between 0 and 1.  

If you square any decimal number in this range you will get an answer less than 1.  Try = 0.998.

Therefore Quantity B is always larger.

Example Question #371 : Arithmetic

Which is greater, when 

Quantity A

Quantity B

Possible Answers:

Quantity B is greater

Quantity A is greater

The relationship cannot be determined from the information given

The two quantities are equal

Correct answer:

The relationship cannot be determined from the information given

Explanation:

When  must be a decimal. Therefore it will decrease when it is squared. To find this answer we can substitute two values for .

 and 

When 

But when 

Therefore we cannot tell which is greater based on the information given.

 

Example Question #1 : How To Square A Decimal

Which is greater, when 

Quantity A

Quantity B

Possible Answers:

Quantity A is greater

The two quantities are equal

Quantity B is greater

The relationship cannot be determined from the information given

Correct answer:

The relationship cannot be determined from the information given

Explanation:

When  must be a decimal. Therefore it will decrease when it is squared. To find this answer we can substitute two values for .

 and 

When 

But when 

Therefore we cannot tell which is greater based on the information given.

 

Example Question #2 : Basic Squaring / Square Roots

Which is greater, when 

Quantity A

Quantity B

Possible Answers:

The relationship cannot be determined from the information given

Quantity B is greater

Quantity A is greater

The two quantities are equal

Correct answer:

Quantity A is greater

Explanation:

When  must be a negative decimal. Therefore it will decrease when it is squared and become positive. The first quantity  is the distance to 0 from , in other words the positive value of . The second quantity  will always be positive, but because it is a decimal it will always be less than , if  was a positive quantity. Since , then  wiill always be greater than .

Quantity A is greater.

Example Question #1 : Basic Squaring / Square Roots

Which is greater, when 

Quantity A

Quantity B

Possible Answers:

The relationship cannot be determined from the information given

Quantity B is greater

Quantity A is greater

The two quantities are equal

Correct answer:

Quantity B is greater

Explanation:

When  must be a negative decimal. Therefore it will decrease when it is squared and become positive. Because  must be a decimal,  will also be a decimal. Therefore  will never be greater than 1.

Quantity B is greater.

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

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