Originally Posted by

**Chop Suey** Hi Amero!

You didn't get problem 1a) correct. Let's remember some properties of radicals quickly (it's actually properties of exponents, but for fractional exponents):

$\displaystyle \sqrt[n]{A \cdot B} = \sqrt[n]{A} \cdot \sqrt[n]{B}$

$\displaystyle \sqrt[n]{\frac{A}{B}} = \frac{\sqrt[n]{A}}{\sqrt[n]{B}}$

Back to 1.a)

$\displaystyle \sqrt{\frac{48a}{20a^4}}$

$\displaystyle = \frac{\sqrt{48a}}{\sqrt{20a^4}}$

$\displaystyle = \frac{\sqrt{48}\sqrt{a}}{\sqrt{20}\sqrt{a^4}}$

$\displaystyle = \frac{\sqrt{3 \cdot 16}\sqrt{a}}{\sqrt{4 \cdot 5}\sqrt{a^2 \cdot a^2}}$

$\displaystyle = \frac{4\sqrt{3a}}{2a{\color{red}^2}\sqrt{5}}$