1. **State the problem:** Factor the expression $$x^2 - \sqrt{81}$$. 2. **Simplify the square root:** $$\sqrt{81} = 9$$. 3. **Rewrite the expression:** $$x^2 - 9$$. 4. **Recognize the difference of squares:** The expression is of the form $$a^2 - b^2$$ where $$a = x$$ and $$b = 3$$. 5. **Use the difference of squares formula:** $$a^2 - b^2 = (a - b)(a + b)$$. 6. **Apply the formula:** $$x^2 - 9 = (x - 3)(x + 3)$$. **Final answer:** $$(x - 3)(x + 3)$$.