How do you simplify the expression 4 over square root of 7 + the square root of 3? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer Alan P. Sep 15, 2015 # (sqrt(7) - sqrt(3))# Explanation: #4/(sqrt(7)+sqrt(3))# #color(white)("XXXXX")#rationalizing the denominator: #=4/(sqrt(7)-sqrt(3))xx(sqrt(7)+sqrt(3))/(sqrt(7)+sqrt(3))# #=(4(sqrt(7)+sqrt(3)))/((sqrt(7))^2-(sqrt(3))^2)# #=(4(sqrt(7)+sqrt(3)))/(7-3)# #=(cancel(4)(sqrt(7)+sqrt(3)))/cancel(4)# 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 1267 views around the world You can reuse this answer Creative Commons License