Weird square root problem? GMAT. What the fastest way to crack it?

Question

For what value X, is the answer not a real number when you have:

sqrt of (sqrt 1 minus sqrt of 2 minus square root of x )

A: 1
B: 2
C: 3
D: 4
E: 5

Answer 1

I assume you mean sqrt(sqrt(1-sqrt(2-sqrt(x))), because other interpretations are possible.

The key is to avoid taking the square root of a negative number. This will not happen with the given choices, except x=5, because then you have sqrt(5)=2.236, and then you're computing sqrt(2-2.236)=sqrt(-0.236), which is not a real number.

Answer 2

The square root of a negative number is not a real number. So you want to look for the value of X that makes the expression in the parantheses negative. However, the expression inside the parantheses would always be negative, as the sqrt(1) minus the sqrt(2) is negative to begin with and since the square root of anything is positive, subtracting that would make it negative no matter what X is.

Answer 3

at a glance we see that if 2-sqrt(x) <0, we will not have real number... this can happen when sqrt(x)>2 or x>4; so here x= 5

Answer 4

sqrt of - 1 = i (non - real number) since sq of (i) = - 1

the value of x = 2

Answer 5

E,
but actually your question is not clear at all
please write all the parenthesis