Question

How do you rationalize the denominator and simplify `1/sqrt3`?

Answer 1

So we want to "rationalize" the denominator by removing the `sqrt3` from the denominator, and replace it with a whole number.

Well, how can we manipulate the radical into a whole number?

Maybe we can multiply both the top and the bottom by the same number, and rationalize the bottom by doing so?

If you recall, `sqrt3 * sqrt3 = 3`

So, we can multiply both the top and the bottom by `sqrt3 / sqrt3` to make the bottom into 3!!

`1/sqrt3 * (sqrt3 / sqrt3)`

Since `sqrt3 / sqrt3 = 0` we haven't changed the value of anything, so this is good.

We finally have `sqrt3 / 3`