How do we rationalize a denominator?

1 Answer
reudhreghs
Apr 3, 2016

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).

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