Question

How do you rationalize the denominator and simplify `(5+sqrt3)/(2-sqrt3)`?

Answer 1

`color(green)(13+7sqrt(3))`

Explanation:

We can rationalize the denominator by multiplying the numerator and the denominator by the conjugate of the denominator.

The conjugate of `(2-sqrt(3))` is `(2+sqrt(3))`

`(5+sqrt(3))/(2-sqrt(3)) xx (2+sqrt(3))/(2+sqrt(3))`

`color(white)("XXX")=(13+7sqrt(3))/(2^2-(sqrt(3))^2)=13+7sqrt(3)`