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

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Answer 1 · 2018-05-14T15:27:06

$sqrt(5)$

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

$a/b : c/d = a/b \cdot d/c$

So, in your case,

$sqrt(2)/sqrt(8) : sqrt(2)/sqrt(40) = sqrt(2)/sqrt(8) \cdot sqrt(40)/sqrt(2)$

We can cross-cancel $sqrt(2)$ :

$cancel(sqrt(2))/sqrt(8) \cdot sqrt(40)/cancel(sqrt(2)) = sqrt(40)/sqrt(8)$

Finally, remembering that $sqrt(ab)=sqrt(a)sqrt(b)$ , we have

$sqrt(40)/sqrt(8) = sqrt(5 \cdot 8)/sqrt(8) = (sqrt(5)\cdot cancel(sqrt(8)))/cancel(sqrt(8)) = sqrt(5)$

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