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

1 Answer
Nov 7, 2016

(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!