# Thread: Th e square root of a negative number is not a real number.

1. ## Th e square root of a negative number is not a real number.

Hi!

I came across this - "The square root of a negative number is not a real number."

I used to think that all numbers are real number (Positive/Negative/Rational/Irrational/Integer) Requesting the members to respond with lucid explanation if possible. Also, it would be great if someone can forward a link that lists Number Properties.

Thanks
TARUN  Reply With Quote

2. This is true: the square root of a negative number is not a real number. The square root of a negative number is called a complex number (it's also referred to as an imaginary number)
On the GMAT, we are told to limit our mathematics to real number. So, for example, if we are told to solve x^2 = -4 for x, we know that x = root(-4) or x = -root(-4). Since root(-4) is not a rel number, we say (when taking the GMAT) that this equation has no solution.

As far as a list of Number Properties goes, the Official Guide explains everything you need to know.

Cheers,
Brent
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3. Thanks Brent.
Is there a strategy to solve number property questions? While reading the properties, they seem easy and doable. However, wen framed in ques they seem so highly confusing.  Reply With Quote

4. On similar lines, I find that x^2 +5=0 has no solution. Since, x^2 + 5 is always greater than 1.

Thanks Brent  Reply With Quote

5. Originally Posted by tarunlakhani Thanks Brent.
Is there a strategy to solve number property questions? While reading the properties, they seem easy and doable. However, wen framed in ques they seem so highly confusing.
That's a very open-ended question with no easy answer.
That said, I feel that many number (integer) properties questions can be solved using prime factorization.

Cheers,
Brent
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