What is the use of rationalizing the denominator?

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What is the use of rationalizing the denominator?

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Answer 1 · 2015-03-31T03:35:54

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

$\sqrt{2} \approx 1.414$ $sqrt2 ~~ 1.414$ For a decimal approximation would you rather do $\frac{1}{\sqrt{2}} = 1 \div 1.414$ $1/sqrt2 = 1 -: 1.414$ or $\frac{\sqrt{2}}{2} = 1.414 \div 2$ $sqrt2/2 = 1.414 -:2$

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 $\frac{77}{154}$ $77/154$ ?
Well, really the problem is, that's not how we spell $\frac{1}{2}$ $1/2$ If you and I are solving a problem and I write $\frac{77}{154}$ $77/154$ and you write $\frac{86}{746}$ $86/746$ 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 $\frac{x - 9}{\sqrt{x} - 3} = \sqrt{x} + 3$ $(x-9)/(sqrtx-3) = sqrtx+3$ .

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What is the use of rationalizing the denominator?

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