1. **State the problem:** Find the zeroes of the quadratic expression $x^2 - 3$. 2. **Formula and rule:** To find zeroes, set the expression equal to zero and solve for $x$: $$x^2 - 3 = 0$$ 3. **Solve the equation:** Add 3 to both sides: $$x^2 = 3$$ 4. **Take the square root:** $$x = \pm \sqrt{3}$$ 5. **Interpretation:** The zeroes of the expression are the values of $x$ where the expression equals zero, which are $x = \sqrt{3}$ and $x = -\sqrt{3}$. **Final answer:** The zeroes are $\boxed{\pm \sqrt{3}}$.