If x < 0, then sqrt(-x|x|) is

[roshin.nair]

Ron,
Why cant sqrt of 16 be -4?. Does the value function returns got any thing to do with what range of values x holds?

Thanks,
Roshin

[jnelson0612]

Ron,
Why cant sqrt of 16 be -4?. Does the value function returns got any thing to do with what range of values x holds?

Thanks,
Roshin

Hi Roshin,
This is a part of the test that confuses people. Here are the GMAT rules about this:
1) The square root of a number is the positive number only. Thus, the square root of 16 is ONLY positive 4 on the GMAT.
*however*
2) If I have x^2 = 16, then x could be 4 or -4.

Just remember this:
--if squaring, then the value being squared could be positive or negative
--if square rooting, the result can only be positive

I hope that this helps!

[RonPurewal]

^^^^ this.

i just want to add that this is not a "GMAT thing".

the "√" symbol can only represent a non-negative value -- absolutely anywhere mathematics is done, anywhere in the world.

the reason is, basically, that symbols (like "√") become meaningless if they have more than one interpretation. so, for "√" to be a useful concept at all, it has to have exactly one meaning all the time -- and that meaning happens to be the non-negative root.

--

by contrast, when you say "Solve x^2 = 16", you are not using a symbol with a special meaning -- i.e., there is no "√" anywhere in those directions.
in that case, you're just looking for any and all x's that actually make x^2 = 16 a true statement. so, here, both 4 and -4 work.