# GRE Math : Basic Squaring / Square Roots

## Example Questions

← Previous 1

### Example Question #1 : Basic Squaring / Square Roots

Which quantity is greater? When

Quantity A

Quantity B

1

The relationship cannot be determined from the information given.

Quantity B is greater.

Quantity A is greater.

The two quantities are equal.

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 #1 : Basic Squaring / Square Roots

Which is greater, when

Quantity A

Quantity B

The two quantities are equal

Quantity A is greater

Quantity B is greater

The relationship cannot be determined from the information given

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 #3 : Basic Squaring / Square Roots

Which is greater, when

Quantity A

Quantity B

Quantity A is greater

The two quantities are equal

Quantity B is greater

The relationship cannot be determined from the information given

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

Quantity B is greater

The relationship cannot be determined from the information given

Quantity A is greater

The two quantities are equal

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 #5 : Basic Squaring / Square Roots

Which is greater, when

Quantity A

Quantity B

The relationship cannot be determined from the information given

Quantity A is greater

The two quantities are equal

Quantity B is greater

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 : Basic Squaring / Square Roots

Find the square root of the following decimal:

Explanation:

The easiest way to find the square root of a fraction is to convert it into scientific notation.

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

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

Find the square root of the following decimal:

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:

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 #31 : Decimals

Find the square root of the following decimal:

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: