Tricky Gprep

[Shag]

Q. For which of the following values of x is Sqrt {1-Sqrt 2 -(Sqrt x)} not defined as a real number ?

-1
-2
-3
-4
-5

[suyash]

ROOT 5 is more than 2 and since it becomes negative,square root of a negative is not defined.It is always better to know few of these like root 2,3,5,7 etc...

[RonPurewal]

ROOT 5 is more than 2 and since it becomes negative,square root of a negative is not defined.It is always better to know few of these like root 2,3,5,7 etc...

that's the idea.

here's a stronger (and perhaps clearer) phrasing: you aren't allowed to take square roots of negative numbers.
therefore, the easiest way to do this problem is just to plug in the answer choices, and note which answer choice ends up compelling division by a negative. in this case, it's answer choice e, because, as the above poster has written, (2 - rad 5) is a negative quantity.

know your number properties! remember that the test is not going to rely on calculation: i.e., the test doesn't care whether you can estimate the value of rad(5) or rad(3) or whatever else. it's the number properties (such as 'can't take roots of negatives') that count.