Question

How do we rationalize a denominator?

Answer 1

Multiply the whole fraction by the denominator over itself.

Explanation:

If you have a fraction where the denominator (bottom number) is irrational, such as a square root, then multiply the whole fraction by the denominator divided by itself.

Take the example

`5/sqrt2`

which has a rational denominator.

Multiply the entire fraction by the denom. divided by itself, like so

`5/sqrt 2 * sqrt2/sqrt2 = (5sqrt2)/2`

More examples are

`3/sqrt7 * sqrt7/sqrt7 = (3sqrt7)/7`

`5/sqrt18 = 5/(3sqrt2)`
`5/(3sqrt2) * sqrt2/sqrt2 = (5sqrt2)/6`

In this last example I turned `sqrt18` into `3sqrt2` by laws of surds, and then, because `3` is already rational, I only multiplied by `sqrt2/sqrt2`, not `(3sqrt2)/(3sqrt2)`.