How do you rationalize the denominator and simplify (sqrt (77))/ (sqrt (35))?

2 Answers
Apr 19, 2015

In this way:

sqrt77/sqrt35=sqrt77/sqrt35*sqrt35/sqrt35=sqrt(77*35)/35=

=sqrt(7*11*5*7)/35=(7*sqrt55)/35=sqrt55/5.

OR:

sqrt77/sqrt35=sqrt(77/35)=sqrt(11/5)=sqrt11/sqrt5*sqrt5/sqrt5=sqrt55/5.

OR:

sqrt77/sqrt35=(sqrt7*sqrt11)/(sqrt7*sqrt5)=sqrt11/sqrt5*sqrt5/sqrt5=sqrt55/5.

Apr 19, 2015

sqrt(77)/sqrt(35)

=(sqrt(11)sqrt(7))/(sqrt(5)sqrt(7))

=sqrt(11)/sqrt(5)

=sqrt(11)/sqrt(5)*sqrt(5)/sqrt(5)

=(sqrt(11)sqrt(5))/5

=sqrt(55)/5