Answer
$a)$ $\dfrac{\sqrt{6}}{6}$
$b)$ $\dfrac{\sqrt{6}}{2}$
$c)$ $\dfrac{9\sqrt[4]{8}}{2}$
Work Step by Step
$a)$ $\dfrac{1}{\sqrt{6}}$
Multiply the numerator and the denominator by $\sqrt{6}$ and simplify:
$\dfrac{1}{\sqrt{6}}=\dfrac{1}{\sqrt{6}}\cdot\dfrac{\sqrt{6}}{\sqrt{6}}=\dfrac{\sqrt{6}}{\sqrt{6^{2}}}=\dfrac{\sqrt{6}}{6}$
$b)$ $\sqrt{\dfrac{3}{2}}$
Rewrite as $\dfrac{\sqrt{3}}{\sqrt{2}}$:
$\sqrt{\dfrac{3}{2}}=\dfrac{\sqrt{3}}{\sqrt{2}}=...$
Multiply the numerator and the denominator by $\sqrt{2}$ and simplify:
$...=\dfrac{\sqrt{3}}{\sqrt{2}}\cdot\dfrac{\sqrt{2}}{\sqrt{2}}=\dfrac{\sqrt{6}}{\sqrt{2^{2}}}=\dfrac{\sqrt{6}}{2}$
$c)$ $\dfrac{9}{\sqrt[4]{2}}$
Multiply the numerator and the denominator by $\sqrt[4]{2^{3}}$ and simplify:
$\dfrac{9}{\sqrt[4]{2}}=\dfrac{9}{\sqrt[4]{2}}\cdot\dfrac{\sqrt[4]{2^{3}}}{\sqrt[4]{2^{3}}}=\dfrac{9\sqrt[4]{2^{3}}}{\sqrt[4]{2^{4}}}=\dfrac{9\sqrt[4]{8}}{2}$
