real number problem

For which of the following values of x is (1-((2-((x)^1/2))^1/2))^1/2 not defined as the real number.

Answers:

1
2
3
4
5

to answer this question you shd knw the definition of real number...
If the number doesnt exist or its an imaginary number then its not a real number
such as (-3)^1/2

subst x =5 (squr root of 5 is >2)
(2-(2.23))^1/2 which doesnt exist
you can try other choices tooo

I will go with 5

nailyad,

I understand your logic for number 5... the square root of any negative number is imaginary. My question is, how would you remove 4 as a possiblity? With x as 4, you would get:

a) sqrt(1-(sqrt(2- 2))

OR

b) sqrt(1-(sqrt(2- (-2)) (Remeber that a square root can be the positive or negative)

In scenario a, the answer from there would end up being sqrt(1-0)... which would just equal 1.

In scenario b, the answer would be sqrt(1-(sqrt4)) = sqrt(1-2) = sqrt(-1)... Also NOT a real number!!!! Does anyone else see this, or am I doing something wrong here?

NOTE: I haven't done the math, but I believe the same would hold true for 2 and 3...