root of negative number?

[yamini]

some where I read root of negative number is undefined.

According to the OG10, cube root of -89 is between -4 and -5.

In this case what is sqrt(-4) ?

[StaceyKoprince]

You will not see a square root sign with a negative number underneath it on the test - this is an example of an imaginary number and imaginary numbers are not tested on the GMAT. (This does not mean that you won't see something like x^2 = 16 and you have to solve that as +4 and -4. But notice that what I just typed in the previous sentence does not include a square root sign.)

A cube maintains the sign of the original number. A square does not; instead, a square is always positive. So you can take the cube root of a negative number, but not the square root of a negative number because, by definition, a square of a real number is always positive.