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{√((2^2)\cdot 5\cdot w^2\cdot w^1)}{√(3^2)}\implies \cfrac{2^2\cdot w√(5\cdot w^1)}{3}\implies \cfrac{4w√(5w)}{3}`