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.

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