How do you simplify #sqrt3 - 2sqrt3#?

1 Answer
Don't Memorise
Sep 4, 2015

#=color(blue)(-9#

Explanation:

#sqrt3 -2sqrt3# can be simplified by multiplying the expression by its the conjugate which #=color(blue)(sqrt3 +2sqrt3#

=#(sqrt3 -2sqrt3 )* (color(blue)(sqrt3 +2sqrt3))#

Now, we can apply the property :
#(a-b)(a+b) = color(blue)(a^2-b^2#

#(sqrt3 -2sqrt3 )* (color(blue)(sqrt3 +2sqrt3)) = (sqrt3)^2 - (2sqrt3)^2#
#=3- 4*3 #
#=3-12#
#=color(blue)(-9#

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