How do you simplify #(3+6sqrt3) / (5 + 12sqrt3)#? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer Vivek A. Jan 18, 2017 #"3 + 6√3"/"5 + 12√3" = "(201 + 6√3)"/"407"# Explanation: #"3 + 6√3"/"5 + 12√3"# Rationalising the denominator #"3 + 6√3"/"5 + 12√3" × "5 - 12√3"/"5 - 12√3"# #"(3 + 6√3)(5 - 12√3)"/"(5 + 12√3)(5 - 12√3)"# #"(3)(5) - (3)(12√3) + (6√3)(5) - (6√3)(12√3)"/((5)^2 - (12√3)^2# #"15 - 36√3 + 30√3 - 216"/"25 - 432"# #"-201 - 6√3"/"-407"# #"-(201 + 6√3)"/"-407"# #"(201 + 6√3)"/"407"# 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 1442 views around the world You can reuse this answer Creative Commons License