How do you simplify #sqrt(18/5)#?

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Answer 1 · 2018-04-07T15:21:05

See a solution process below:

First, we can rewrite and simplify the numerator as:

#sqrt(18)/sqrt(5) => sqrt(9 * 2)/sqrt(5) => (sqrt(9)sqrt(2))/sqrt(5) => (3sqrt(2))/sqrt(5)#

Now, if necessary, we can rationalize the denominator by multiplying the fraction by the appropriate form of #1#:

#sqrt(5)/sqrt(5) xx (3sqrt(2))/sqrt(5) =>#

#(sqrt(5) xx 3sqrt(2))/(sqrt(5) xx sqrt(5)) =>#

#(3sqrt(5)sqrt(2))/5 =>#

#(3sqrt(5 xx 2))/5 =>#

#(3sqrt(10))/5#

Or

#3/5sqrt(10)#