Question #1f341

1 Answer
Aug 29, 2017

(13 +3sqrt3 +sqrt5 +2sqrt15 )/11

Explanation:

The problem is about rationalising the denominator. to do this, multiply with the conjugate in numerator and denominator like this:

1/(1+sqrt3 -sqrt5) *(1+sqrt3 +sqrt5)/(1+sqrt3 +sqrt5)

= (1+sqrt3 +sqrt5)/((1+sqrt3)^2 - (sqrt5)^2)

=(1+sqrt3 +sqrt5)/(4+2sqrt3 -5)

=(1+sqrt3 +sqrt5)/(2sqrt3 -1)

Now again multiply with the conjugate

(1+sqrt3 +sqrt5)/(2sqrt3-1) *(2sqrt3 +1)/(2sqrt3 +1)

(2sqrt3 +12 +2sqrt15 +1+sqrt3 +sqrt5)/11

(13 +3sqrt3 +sqrt5 +2sqrt15 )/11