Question

How do you rationalize the denominator and simplify `6/(sqrt4+sqrt5)`?

Answer 1

`6(sqrt5+-2)`

Explanation:

Multiply numerator and denominator by the conjugate `sqrt5-sqrt4` of the denominator and use `(a-b)(a+b)=(a^2-b^2)`. Hence,

#6/(sqrt5+2)=(6(sqrt5-2))/ ((sqrt5-2)(sqrt5+2))# or

`(6(sqrt5-2))/(5-4)` or

`6(sqrt5-2)`