Question

PLEASE HELP!!! MATH!!! Question attached!! Simplify the radical expression.

Answer 1

$\bf \sqrt{\cfrac{80w^3}{9}}\qquad \begin{cases} 80=2\cdot 2\cdot 2\cdot 2\cdot 5\\ \qquad 2^2\cdot 2^2\cdot 5\\ \qquad (2^2)^2\cdot 5\\ w^3=w^{2+1}\\ \qquad w^2\cdot w^1\\ 9=3\cdot 3\\ \qquad 3^2 \end{cases}\implies \sqrt{\cfrac{(2^2)\cdot 5\cdot w^2\cdot w^1}{3^2}} \\\\\\ \cfrac{\sqrt{(2^2)\cdot 5\cdot w^2\cdot w^1}}{\sqrt{3^2}}\implies \cfrac{2^2\cdot w\sqrt{5\cdot w^1}}{3}\implies \cfrac{4w\sqrt{5w}}{3}$