\( \Large \left[ \left(\frac{p}{q} \right)^{-1} \right]^{-1} \) =\( \Large \left[\frac{1}{p/q} \right]^{-1} \) =\( \Large \left[ \frac{q}{p} \right]^{-1}\) =\( \Large \frac{1}{q/p}\) =\( \Large \frac{p}{q} \)
If n is even, then square root will contain \( \Large \frac{n}{2}\) digits. If n is odd, then square root will contain \( \Large \frac{n+1}{2} \) digits.
\( \Large \sqrt[3]{343} \times \sqrt[3]{-125} \) =\( \Large \sqrt[3]{343 \times \left( -125 \right)} \) =\( \Large - \sqrt[3]{7 \times 7 \times 7 \times 5 \times 5 \times 5} \) =\( \Large - \left( 7 \times 5 \right) \) = -35
\( \Large \frac{9}{\sqrt{11} + \sqrt{2}} \) = \( \Large \frac{9}{\sqrt{11} + \sqrt{2}} \times \frac{\sqrt{11} - \sqrt{2}}{\sqrt{11} - \sqrt{2}}\) =\( \Large \frac{9\left(\sqrt{11} - \sqrt{2}\right)}{11- 2} \) =\( \Large \frac{9\left(\sqrt{11} - \sqrt{2}\right)}{9} \) = \( \sqrt{11} - \sqrt{2} \)