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

1 Answer
Feb 18, 2016

Answer:

Multiply by the conjugate surd of the denominator.

#frac{2}{5-sqrt3} = frac{5+sqrt3}{11}#

Explanation:

The conjugate surd of #5-sqrt3# is #5+sqrt3#.

#frac{2}{5-sqrt3} = frac{2}{5-sqrt3}*frac{5+sqrt3}{5+sqrt3}#

#= frac{2(5+sqrt3)}{(5)^2-(sqrt3)^2}#

#= frac{2(5+sqrt3)}{25-3}#

#= frac{2(5+sqrt3)}{22}#

#= frac{5+sqrt3}{11}#