How do you simplify # \frac { 2} { 1+ \sqrt { 3} - \sqrt { 12} }#?

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Answer 1 · 2017-10-24T12:53:04

#=-1-sqrt(3)#

#2/(1+sqrt(3)-sqrt(12))#

Now, #sqrt(12)=sqrt(4*3)=sqrt(4)*sqrt(3)=2sqrt(3)#

#=2/(1+sqrt(3)-2sqrt(3))#
#=2/(1-sqrt(3))#

Multiply by #(1+sqrt(3))/(1+sqrt(3))# to eliminate the radical in the denominator.

#=2/(1-sqrt(3))*(1+sqrt(3))/(1+sqrt(3))#

Remember that #(a+b)*(a-b)=a^2-b^2#.

#=(2(1+sqrt(3)))/(1^2-sqrt(3)^2)#
#=(2+2sqrt(3))/(1-3)#
#=(2+2sqrt(3))/-2#
#=-1-sqrt(3)#