Question

What is the following quotient?

Answer 1

`(√(3) )/(4)`

Explanation:

`(1)/(1+√(3) )`

basically we want to get rid of the √3 on the denominator

to do so we multiply it by itself so it is a perfect square

but whatever we do to the top we must do to the bottom so we multiply the numerator and denominator by √3

`(1*√(3) )/(1+√(3)*√(3) )=(√(3) )/(1+√(9) ) =(√(3) )/(1+3) =(√(3) )/(4)`

notes : √3 × √3 = √9 which is a perfect square that simplfies to 3