Answer
$a)$ $4\sqrt{3}$
$b)$ $\dfrac{2\sqrt{15}}{5}$
$c)$ $\dfrac{8\sqrt[3]{5}}{5}$
Work Step by Step
$a)$ $\dfrac{12}{\sqrt{3}}$
Multiply the numerator and the denominator by $\sqrt{3}$ and simplify:
$\dfrac{12}{\sqrt{3}}=\dfrac{12}{\sqrt{3}}\cdot\dfrac{\sqrt{3}}{\sqrt{3}}=\dfrac{12\sqrt{3}}{\sqrt{3^{2}}}=\dfrac{12\sqrt{3}}{3}=4\sqrt{3}$
$b)$ $\sqrt{\dfrac{12}{5}}$
Rewrite as $\dfrac{\sqrt{12}}{\sqrt{5}}$:
$\sqrt{\dfrac{12}{5}}=\dfrac{\sqrt{12}}{\sqrt{5}}=...$
Multiply the numerator and the denominator by $\sqrt{5}$ and simplify:
$...=\dfrac{\sqrt{12}}{\sqrt{5}}\cdot\dfrac{\sqrt{5}}{\sqrt{5}}=\dfrac{\sqrt{60}}{\sqrt{5^{2}}}=\dfrac{\sqrt{15\cdot4}}{5}=\dfrac{2\sqrt{15}}{5}$
$c)$ $\dfrac{8}{\sqrt[3]{5^{2}}}$
Multiply the numerator and the denominator by $\sqrt[3]{5}$ and simplify:
$\dfrac{8}{\sqrt[3]{5^{2}}}=\dfrac{8}{\sqrt[3]{5^{2}}}\cdot\dfrac{\sqrt[3]{5}}{\sqrt[3]{5}}=\dfrac{8\sqrt[3]{5}}{\sqrt[3]{5^{3}}}=\dfrac{8\sqrt[3]{5}}{5}$
