1. Is it true that $\sqrt{ab} = \sqrt{a}\sqrt{b}$ for all non-negative values of $a$ and $b$?
2. Decide whether the statement is true or false: $\sqrt{12} = \sqrt{8} + \sqrt{4}$.
3. Is it true that $\sqrt{\frac{a}{b}} = \frac{\sqrt{a}}{\sqrt{b}}$ for all $a \ge 0, b > 0$?
4. Is it true that $\sqrt{a + b} = \sqrt{a} + \sqrt{b}$ for all non-negative values of $a$ and $b$? Test with the case where $a=9$ and $b=16$.
5. Is it true that $\sqrt{a - b} = \sqrt{a} - \sqrt{b}$ for all $a \ge b \ge 0$? Test with the case where $a=100$ and $b=36$.
6. Decide whether the statement is true or false. Assume all variables are positive. $\sqrt{1 + 25r^2} = 1 + 5r$.
7. Decide whether the statement is true or false. Assume all variables are positive. $\sqrt{4a^2 + b^2} = 2a + b$.
8. Decide whether the statement is true or false. Assume all variables are positive. $\sqrt{4s^2 - 1} = 2s - 1$.
9. Decide whether the statement is true or false: $\sqrt{12} = \sqrt{4}\sqrt{3}$.