Question

What is the use of rationalizing the denominator?

Answer 1

In ancient times (when I was a student ) we did arithmetic with pencil and paper.

`sqrt2 ~~ 1.414` For a decimal approximation would you rather do `1/sqrt2 = 1 -: 1.414` or `sqrt2/2 = 1.414 -:2`

Now that only hard-cores do arithmetic with pencil and paper, I think of it as a spelling rule. I think of reducing fractions as a spelling rule as well.

What is wrong with writing `77/154`?
Well, really the problem is, that's not how we spell `1/2` If you and I are solving a problem and I write `77/154` and you write `86/746` did we get the same number or different numbers? (they are different)

Rationalizing denominators are similar at the algebra level.

For understanding calculus it becomes quite important to understand why `(x-9)/(sqrtx-3) = sqrtx+3`.