How do you rationalize the following problem 1/ (1+ square root of 3 - square root of 5)? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer Sasha P. Sep 16, 2015 #-(sqrt3+sqrt5)/2# Explanation: #1/(sqrt3-sqrt5)=1/(sqrt3-sqrt5) (sqrt3+sqrt5)/(sqrt3+sqrt5)=# #=(sqrt3+sqrt5)/((sqrt3)^2-(sqrt5)^2)=(sqrt3+sqrt5)/(3-5)=# #=(sqrt3+sqrt5)/-2=-(sqrt3+sqrt5)/2# 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 1526 views around the world You can reuse this answer Creative Commons License