# GRE Math : How to square a decimal

## Example Questions

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

Which quantity is greater? When

Quantity A

Quantity B

1

The two quantities are equal.

Quantity B is greater.

The relationship cannot be determined from the information given.

Quantity A is greater.

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 #1 : How To Square A Decimal

Which is greater, when

Quantity A

Quantity B

The two quantities are equal

The relationship cannot be determined from the information given

Quantity A is greater

Quantity B is greater