Question

How do you simplify `5/(sqrt6+sqrt3)`?

Answer 1

See a solution process below below:

Explanation:

To simplify this we can rationalize the denominator. Or, in other words, remove the radicals from the denominator.

To remove the radicals we need to multiply by the appropriate form of `1`. Remember that `(color(red)(x) + color(blue)(y))(color(red)(x) - color(blue)(y)) = color(red)(x)^2 - color(blue)(y)^2` we can multiply this expression as:

`(sqrt(6) - sqrt(3))/(sqrt(6) - sqrt(3)) xx 5/(sqrt(6) + sqrt(3)) =>`

`(5(sqrt(6) - sqrt(3)))/((sqrt(6))^2 - (sqrt(3))^2) =>`

`(5(sqrt(6) - sqrt(3)))/(6 - 3) =>`

`(5(sqrt(6) - sqrt(3)))/3`

Or

`5/3(sqrt(6) - sqrt(3))`