# Question: Ordering Powers of -0.5

## Comment on Ordering Powers of -0.5

### Isnt root of a negative

Isnt root of a negative number an imaginary number? (which is neither negative nor positive) ### The SQUARE root of a negative

The SQUARE root of a negative number an imaginary number. However, this question features a CUBE root, and we CAN find cube roots of negative numbers.
For example, the cube root of -8 equals -2, since (-2)^3 = -8

### Quick question, not just a sq

Quick question, not just a sq rt but any even root of a negative number is imaginary right? ### That's correct.

That's correct.
If n is an EVEN integer, then the nth root of a negative number will be an IMAGINARY (aka COMPLEX) number.

ASIDE: For students who are wondering what this is all about, please note that imaginary (complex) numbers are not tested on the GRE.

### Hi Brent,

Hi Brent,
Please if you can check for the ques https://greprepclub.com/forum/x-0-and-y-12521.html

OA is A , but can I try this way

√{x²y²}= √{(-xy)²}= -xy = negative value i.e QTY A = QTY B

Let x = -5 and y = 4
Then √{(-5)²(2)²}= √{(-5*2)²} = -10
However, √{x² y²} = positive value as the sq root of positive numbers will always be positive i.e QTY A > QTY B I'm not sure what you're doing when you write the following:
√{x²y²} = √{(-xy)²} = -xy = negative value

How did xy become -xy?
Is it because we're told x < 0?
If so, then -x represents a POSITIVE value.
For example, if x = -2, then -x = -(-2) = 2

So, that's one issue with your solution.

There's also a problem when you write: √{(-5)²(2)²}= √{(-5*2)²} = -10
The √ notation tell us to take the POSITIVE square root.
For example √25 = 5 and √49 = 7

So, in your example: √{(-5*2)²} = √{(-10)²} = √100 = 10 (not -10)

Here's my full solution: https://greprepclub.com/forum/x-0-and-y-12521.html#p31040

Cheers,
Brent