How do you simplify #frac { 4} { \sqrt { 20} - \sqrt { 12} #?

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Answer 1 · 2018-05-12T11:16:52

# 4/ (sqrt 20- sqrt 12)= sqrt 5+ sqrt 3 #

# 4/ (sqrt 20- sqrt 12)# Multiplying by #(sqrt 20+ sqrt 12)# in

both numerator and denominator we get,

#= (4 (sqrt 20+ sqrt 12))/((sqrt 20- sqrt 12)(sqrt 20+ sqrt 12))#

#= (4 (sqrt 20+ sqrt 12))/((sqrt 20)^2- (sqrt 12)^2)#

#= (4*2 (sqrt 5+ sqrt 3))/(20-12)#

#= ( cancel8(sqrt 5+ sqrt 3))/cancel8#

#= sqrt 5+ sqrt 3# [Ans]