# How do you simplify (sqrt2 /sqrt8) div (sqrt2 /sqrt40)?

May 14, 2018

#### Answer:

$\sqrt{5}$

#### Explanation:

Dividing by a fraction is the same as multiplying by the inverse of the fraction:

$\frac{a}{b} : \frac{c}{d} = \frac{a}{b} \setminus \cdot \frac{d}{c}$

So, in your case,

$\frac{\sqrt{2}}{\sqrt{8}} : \frac{\sqrt{2}}{\sqrt{40}} = \frac{\sqrt{2}}{\sqrt{8}} \setminus \cdot \frac{\sqrt{40}}{\sqrt{2}}$

We can cross-cancel $\sqrt{2}$:

$\frac{\cancel{\sqrt{2}}}{\sqrt{8}} \setminus \cdot \frac{\sqrt{40}}{\cancel{\sqrt{2}}} = \frac{\sqrt{40}}{\sqrt{8}}$

Finally, remembering that $\sqrt{a b} = \sqrt{a} \sqrt{b}$, we have

$\frac{\sqrt{40}}{\sqrt{8}} = \frac{\sqrt{5 \setminus \cdot 8}}{\sqrt{8}} = \frac{\sqrt{5} \setminus \cdot \cancel{\sqrt{8}}}{\cancel{\sqrt{8}}} = \sqrt{5}$