How do you rationalize #5/(sqrt3 +sqrt5)#?

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Answer 1 · 2018-03-09T09:57:46

#(5sqrt5+5sqrt3)/(2)#

we are given #5/(sqrt3+sqrt5)#, to rationalize this multiply both numerator and denominator with #sqrt3-sqrt5#

#5/(sqrt3+sqrt5)## *# #(sqrt3-sqrt5)/(sqrt3-sqrt5)# now notice that

the denominator resembles #a^2-b^2# = #(a+b)*(a-b)#

so #(5sqrt3-5sqrt5)/((sqrt3)^2-(sqrt5)^2#

hence, upon simplifying

#(5sqrt3-5sqrt5)/(-2)#

or
#(5sqrt5+5sqrt3)/(2)#