How do you combine #sqrt 3 - 2#?

1 Answer
George C.
Nov 8, 2015

You cannot simplify this expression.

However, if you need to rationalize it out of a denominator, you can multiply by its conjugate #sqrt(3)+2# to get #-1#

Explanation:

You cannot combine #sqrt(3)# and #-2# in a simple way, but you can multiply #(sqrt(3)-2)# by #(sqrt(3)+2)# to get #-1#.

For example, to simplify a rational expression like:

#(5-2sqrt(3))/(sqrt(3)-2)#

by multiplying both the numerator and denominator by the conjugate #sqrt(3)+2# of the denominator, thus:

#(5-2sqrt(3))/(sqrt(3)-2)=((5-2sqrt(3))(sqrt(3)+2))/((sqrt(3)-2)(sqrt(3)+2))#

#=((10-6)+(5-4)sqrt(3))/(sqrt(3)^2-2^2)#

#=(4+sqrt(3))/(3-4) = (4+sqrt(3))/-1 = -4-sqrt(3)#

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