Question

How do you simplify `5/(sqrt3)` by rationalizing the denominator?

Answer 1

`sqrt3` is not a rational number.
We have been asked to write a fraction equal to this one, but with a rational number for its denominator.

Use the facts that
(1) multiplying by one may change the way a number is written, but it does not change the value of the number and
(2) `sqrt3*sqrt3 = 3`

`5/sqrt3 = 5/sqrt3 * sqrt3/sqrt3 = (5sqrt3)/(sqrt3sqrt3) = (5sqrt3)/3`

`3` is a rational number (in fact it is an integer).