Question

How do you simplify `sqrt ((2x)/(9x))`?

Answer 1

`sqrt((2x)/(9x)) = sqrt(2)/3` excluding `x=0`

Explanation:

For any positive Real numbers `a, b`:

`sqrt(a/b) = sqrt(a)/sqrt(b)`

So we find:

`sqrt((2color(red)(cancel(color(black)(x))))/(9color(red)(cancel(color(black)(x))))) = sqrt(2/3^2) = sqrt(2)/sqrt(3^2) = sqrt(2)/3`

excluding `x=0`, when `sqrt((2x)/(9x)) = sqrt(0/0)` is undefined.