Question 84046
{{{(sqrt(5)+sqrt(55))/(sqrt(5))}}} Start with the given expression


{{{((sqrt(5)+sqrt(55))/(sqrt(5)))((sqrt(5))/(sqrt(5)))}}} Multiply both numerator and denominator by {{{sqrt(5)}}} to rationalize the denominator


{{{(sqrt(5)sqrt(5)+sqrt(5)sqrt(55))/(sqrt(5)sqrt(5))}}} Distribute


{{{(sqrt(5*5)+sqrt(5*55))/(sqrt(5*5))}}} Combine the square roots


{{{(sqrt(25)+sqrt(275))/(sqrt(25))}}} Multiply


{{{(5+sqrt(275))/(5)}}} Take the square root of any perfect squares


{{{(5+sqrt(25*11))/(5)}}} Factor 275 into 25*11


{{{(5+sqrt(25)*sqrt(11))/(5)}}} Break apart the square roots


{{{(5+5*sqrt(11))/(5)}}} Take the square root of 25


{{{5(1+sqrt(11))/(5)}}} Factor out a 5 out of the numerator


{{{cross(5)(1+sqrt(11))/cross(5)}}} Divide


So the expression simplifies to


{{{1+sqrt(11)}}}