Question

How do you simplify `sqrt 2 / sqrt 10`?

Answer 1

`sqrt(2)/sqrt(10) = sqrt(5)/5`

Explanation:

If `a, b >= 0` then `sqrt(a/b) = sqrt(a)/sqrt(b)`

`sqrt(2)/sqrt(10) = sqrt(2/10) = sqrt(1/5) = sqrt(5/25) = sqrt(5)/sqrt(25) = sqrt(5)/5`

Notice that I chose to make the denominator a perfect square `25` in order that the final result has a rational denominator.