How do you simplify #(2+5sqrt3)/(-4+4sqrt2)#?

1 Answer
Nov 7, 2016

Answer:

#(2+2sqrt2+5sqrt3+5sqrt6)/4#

Explanation:

In surd form we must not have surds (roots) in the denominator.
We use the fact that #(a+b)(a-b)=a^2-b^2#

The denominator factorises to #4(-1+sqrt2)#
So we multiply both numerator and denominator by the same thing #(-1-sqrt2)#

#(2+5sqrt3)/(4(-1+sqrt2))# =#(2+5sqrt3)/(4(-1+sqrt2))*((-1-sqrt2)/(-1-sqrt2))#
Numerator#(2+5sqrt3)(-1-sqrt2)=-2-2sqrt2-5sqrt3-5sqrt6#
or #-(2+2sqrt2+5sqrt3+5sqrt6#)

Denominator #4(-1+sqrt2)(-1-sqrt2)=4(1-2)=-4#

Hence answer!