Question

how do I find the domain of the square root of ( x^2 - 3)

Answer 1

You can't take the square root of a negative number and get a real result, so solve:
\[x^2 - 3 \ge 0\]

Answer 2

Given an equation, the domain is the set of all values of x for which the equation is defined in the reals.

\[y =\sqrt{x ^{2}-3}\]

This function has a square root. We know that a square root of a negative number is not defined over reals. Thus the radicand (the expression under the root) must be greater than or equal to zero. Thus

x² − 3 ≥ 0

x² ≥ 3

\[x \le -\sqrt{3}, x \ge \sqrt{3}\]

And this is your domain.

Does that help?

Answer 3

Yes I does. Thank you both for helping me.