How do you simplify #sqrt39/sqrt26#?

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Answer 1 · 2018-04-07T15:42:53

See a solution process below:

First, rewrite the numerator and denominator as:

#sqrt(13 * 3)/sqrt(13 * 2) => (sqrt(13)sqrt(3))/(sqrt(13)sqrt(2))#

We can next cancel the common terms in the numerator and denominator:

#(color(red)(cancel(color(black)(sqrt(13))))sqrt(3))/(color(red)(cancel(color(black)(sqrt(13))))sqrt(2)) => sqrt(3)/sqrt(2)#

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

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

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

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

#sqrt(6)/2#