GMAT Prep 2 PS 24

[kellyeroses]

Can someone help me?

For which of the following values of x is sq root of 1 - sq root of 2 - sq root of x NOT defined as a real number? There is a square root around the entire thing and then around the 2 - x and then around the x.

A 1
B 2
C 3
D 4
E 5

Thanks!

[Stuart@KaplanGMAT]

Pretty much the only non-real numbers are square roots of negative numbers. So, the question is really asking "for which value of x is this expression negative".

I'm having a bit of trouble deciphering where the square roots go from your description (i.e. I'm not sure exactly what the expression is), so I can't actually do the math for you, but the answer has to be either 1 or 5, since extremes are what will make the expression negative.

[simplyjat]

I am assuming that you mentioned

sqrt ( 1 - sqrt ( 2 - sqrt (x) ) )

Square root for positive numbers is real number, whereas square root for negative numbers is complex number. This is asked in the question.

if you consider sqrt ( 2 - sqrt (x) ), it will be complex number (not real number) if 2 <sqrt> 4 satisfies this. The answer is E. 5