chrisontherun wrote:If the square root of t is a real number, is the square root of t positive?
(1) t > 0
(2) t² > 0

If square root of t is a real number, t is non-negative.
Hence, t is either zero or positive.

Now, consider the following two cases,

• square root of t = 1 ---> t = 1 > 0 ---> t² > 0
  square root of t = -1 ---> t = 1 > 0 ---> t² > 0

Both of the above examples satisfy both the statements, but square root of t is positive in the first case and negative in the second case.

The correct answer is E.

chrisontherun wrote:but statement (1), I think is sufficient. I quote wiki: "The principal square root function (usually just referred to as the "square root function") is a function that maps the set of non-negative real numbers onto itself."
if we know the number is positive, the square root is real then the square root is also positive.

There is a difference between square root of x² and √(x²).
There are two square roots of x² : one is positive and the other one is negative. They are x and -x
Among these, the positive one is the 'principal square root' of x². Which is denoted as √(x²).

By definition, √(x²) is always positive and given as |x|.
And two square roots of x² are √(x²) = x and -√(x²) = -x

The portion of Wikipedia you have quoted is actually saying : The principal square root function f(x) = √x (usually just referred to as the "square root function") is a function that maps the set of non-negative real numbers onto itself.
It is actually talking about √x which is different from square root of x, as I have explained earlier.

Hope that helps.

To add to Mitch's post, I thought I'd post an excerpt from the Official Guide:

A square root of a number n is a number that, when squared, is equal to n. The square root of a
negative number is not a real number. Every positive number n has two square roots, one positive
and the other negative, but sqrt(n) denotes the positive number whose square is n. For example, sqrt(9) denotes 3.

Cheers,
Brent