I have no idea how to rationalize this... please help ? ( 2 radicals and one number in the denominator)?

Question

1 / [ 1 + sqrt(3) - sqrt(5) ]

how do you rationalize this T-T...

Answer 1

you can't.. just accept it.

Answer 2

There are a few ways to attack it, but it will be a two step process. One way is to multiply by 1 in the form (1+sqrt(3)-sqrt(5))/(1+sqrt(3)-sqrt(5). In the denominator, the sqrt(5) terms will cancel, Leaving you with only sqrt(3) terms and rational numbers, since sqrt(3)*sqrt(3) = sqrt(9) =3 and sqrt(5)*sqrt(5) = sqrt(25) = 5. Then the problem is reduced to a single radical and a rational in the denominator , which should be simple to finish rationalizing.