Domain of square root of x squared -4

Your function is √(x² - 4).

The part inside the sqrt must be non-negative, thus, solve:  x² - 4 ≥ 0.
Then, algebraically, you get:  x² ≥ 4  --->  |x| ≥ 2  --->  -2>x or 2<x.

Hence, the domain of your function is (-∞,-2) U (2,∞).

((( i.e. from negative infinity to -2, and then from 2 to infinity )))