Question 375045
{{{(sqrt(18)+sqrt(24))/(sqrt(6))}}} Start with the given expression.



{{{(sqrt(3*6)+sqrt(4*6))/(sqrt(6))}}} Factor 18 into 3*6 and factor 24 into 4*6 (notice the presence of 6)



{{{(sqrt(3)*sqrt(6)+sqrt(4)*sqrt(6))/(sqrt(6))}}} Break up the square roots using the identity {{{sqrt(x*y)=sqrt(x)*sqrt(y)}}}



{{{(sqrt(3)*sqrt(6)+2*sqrt(6))/(sqrt(6))}}} Take the square root of 4 to get 2.



{{{(sqrt(6)(sqrt(3)+2))/(sqrt(6))}}} Factor out the GCF {{{sqrt(6)}}}



{{{(highlight(sqrt(6))(sqrt(3)+2))/(highlight(sqrt(6)))}}} Highlight the common terms.



{{{(cross(sqrt(6))(sqrt(3)*sqrt(6)+2))/(cross(sqrt(6)))}}} Cancel out the common terms.



{{{sqrt(3)+2}}} Simplify.



So {{{(sqrt(18)+sqrt(24))/(sqrt(6))=sqrt(3)+2}}}



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