Question

How do you rationalize the denominator and simplify `(sqrt3-sqrt5)/(sqrt5+sqrt3)`?

Answer 1

`sqrt15-4`

Explanation:

You would use the formula:

`(a+b)(a-b)=a^2-b^2`

to razionalize the denominator, then

`(sqrt3-sqrt5)/(sqrt5+sqrt3)=((sqrt3-sqrt5)(sqrt5-sqrt3))/((sqrt5+sqrt3)(sqrt5-sqrt3))=color(red)-((sqrt3-sqrt5)^2)/(5-3)=-(3+5-2sqrt15)/2=(2sqrt15-8)/2=sqrt15-4`