The square root function of $y = x^2 - 2$ can be expressed as:

$y = \sqrt{x^2 - 2}$

This equation describes the positive square root of $x^2 - 2$. The domain of this function will only include values of $x$ for which $x^2 - 2 \geq 0$, meaning $x \leq -\sqrt{2}$ or $x \geq \sqrt{2}$, because the expression inside the square root must be non-negative.

Would you like more details or have any specific questions?

Here are some related questions you might consider:

1. What is the domain and range of the function $y = \sqrt{x^2 - 2}$?
2. How would you graph $y = \sqrt{x^2 - 2}$?
3. Can this function have any negative outputs?
4. How do the solutions of $y = \sqrt{x^2 - 2}$ compare to $y = x^2 - 2$?
5. What is the derivative of $y = \sqrt{x^2 - 2}$?

Tip: Always check the domain of functions involving square roots, ensuring that the expression inside the root is non-negative for real-valued solutions.