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

Question

1447 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2016-04-30T12:12:13

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

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.

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