Question

Simplify by rationalising the denominator : 16 / 4 - under root 32.

Answer 1

$$\begin{gathered} \frac{16}{4-\sqrt{32}}=\frac{16}{4-\sqrt{4^2\times 2}} \\ =\frac{16}{4-4\sqrt{2}} \\ =\frac{4}{1-\sqrt{2}}=\frac{4}{1-\sqrt{2}}\times \frac{1+\sqrt{2}}{1+\sqrt{2}} \\ =\frac{4\left(1+\sqrt{2}\right)}{1^2-{\left(\sqrt{2}\right)}^2}=\frac{4\left(1+\sqrt{2}\right)}{1-2}=-4-4\sqrt{2} \end{gathered}$$