Question 185800
{{{sqrt(33)/sqrt(77)}}} Start with the given expression



{{{(sqrt(33)*sqrt(77))/(sqrt(77)*sqrt(77))}}} Multiply both the numerator and denominator by {{{sqrt(77)}}}



{{{(sqrt(33)*sqrt(77))/(77)}}} Multiply {{{sqrt(77)}}} by {{{sqrt(77)}}} to get {{{77}}}



{{{(sqrt(3*11)*sqrt(11*7))/(77)}}} Factor 33 into 3*11 and factor 77 into 11*7



{{{(sqrt(3*11*11*7))/(77)}}} Combine the roots.



{{{(sqrt(3*11^2*7))/(77)}}} Multiply



{{{(sqrt(3)*sqrt(11^2)*sqrt(7))/(77)}}} Break up the square root



{{{(sqrt(3)*11*sqrt(7))/(77)}}} Take the square root of {{{11^2}}} to get 11



{{{(11*sqrt(3*7))/(77)}}} Recombine the square roots.



{{{(11*sqrt(21))/(77)}}} Multiply



{{{(11*sqrt(21))/(7*11)}}} Factor 77 into 7*11



{{{(cross(11)*sqrt(21))/(7*cross(11))}}} Cancel out the common terms.



{{{sqrt(21)/7}}} Simplify



So {{{sqrt(33)/sqrt(77)=sqrt(21)/7}}}