What is the square root of 27 plus the square root of 75?

##sqrt(27)+sqrt(75)=8sqrt(3)##

If ##a, b >= 0## then ##sqrt(ab) = sqrt(a)sqrt(b)##
##sqrt(27)+sqrt(75)##
##=sqrt(3^2*3)+sqrt(5^2*3)##
##=sqrt(3^2)sqrt(3)+sqrt(5^2)sqrt(3)##
##=3sqrt(3)+5sqrt(3)##
##=(3+5)sqrt(3)##
##=8sqrt(3)##

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