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

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