How do you simplify #18/(6+sqrt(27m))#? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer DaveedSaysHI Apr 12, 2018 #(2sqrt(3m)-4)/m# Explanation: #18/(6+(sqrt(27m))# = #18/((sqrt(27m)+6)# Now #(sqrt(27m)-6)/(sqrt(27m)-6)# is 1 so multiple that to #18/((sqrt(27m)+6)#, #18/((sqrt(27m)+6)#*#(sqrt(27m)-6)/(sqrt(27m)-6)# = #(54sqrt(3m)-108)/(27m)# Now simplify =#(2sqrt(3m)-4)/m# Answer link Related questions How do you simplify #\frac{2}{\sqrt{3}}#? How do you multiply and divide radicals? How do you rationalize the denominator? What is Multiplication and Division of Radicals? How do you simplify #7/(""^3sqrt(5)#? How do you multiply #(sqrt(a) +sqrt(b))(sqrt(a)-sqrt(b))#? How do you rationalize the denominator for #\frac{2x}{\sqrt{5}x}#? Do you always have to rationalize the denominator? How do you simplify #sqrt(5)sqrt(15)#? How do you simplify #(7sqrt(13) + 2sqrt(6))(2sqrt(3)+3sqrt(6))#? See all questions in Multiplication and Division of Radicals Impact of this question 1689 views around the world You can reuse this answer Creative Commons License