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

1 Answer
George C.
Apr 30, 2016

#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.

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