Question

Do you always have to rationalize the denominator?

Answer 1

You should for a final answer, unless the question says otherwise

Answer 2

See below.

Explanation:

Technically no.

The general reason why it is desirable, is to have a standard form. If for example you look a trig ratios that have radicals, these are given with rationalized denominators, so it makes it easier to recognize these ratios when you rationalize the denominator in your calculations. Another reason is before the age of calculators and computers it was considered easier to preform calculations when the denominator was an integer.

Consider this, divide

`5/sqrt(5)`

By hand.

Not easy.

But, after rationalizing:

`(5sqrt(5))/5=sqrt(5)`

The `sqrt(5)` could be found in tables of roots in the early days.