What is the simplified form of square root of 10 - square root of 5 over square root of 10 + square root of 5? Algebra Radicals and Geometry Connections Multiplication and Division of Radicals 1 Answer Alan P. Sep 12, 2015 #(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)=3-2sqrt(2)# Explanation: #(sqrt(10)-sqrt(5))/(sqrt(10)+sqrt(5)# #color(white)("XXX")=cancel(sqrt(5))/cancel(sqrt(5))*(sqrt(2)-1)/(sqrt(2)+1)# #color(white)("XXX")=(sqrt(2)-1)/(sqrt(2)+1)*(sqrt(2)-1)/(sqrt(2)-1)# #color(white)("XXX")=(sqrt(2)-1)^2/((sqrt(2)^2-1^2)# #color(white)("XXX")=(2-2sqrt2+1)/(2-1)# #color(white)("XXX")=3-2sqrt(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 1398 views around the world You can reuse this answer Creative Commons License