Question

Simplify. Divide the radicals.

√80
√20

Answer 1

`\cfrac{√(80)}{√(20)} ~~ \begin{cases} 80=2\cdot 2\cdot 2\cdot 2\cdot 5\\ \qquad 4\cdot 4\cdot 5\\ \qquad 4^2\cdot 5\\ 20=2\cdot 2\cdot 5\\ \qquad 2^2\cdot 5 \end{cases}\implies \cfrac{√(4^2\cdot 5)}{√(2^2\cdot 5)}\implies \cfrac{4√(5)}{2√(5)}\implies \cfrac{4}{2}\cdot \cfrac{√(5)}{√(5)}\implies 2`