In many Algebra textbooks, why rationalizing the denominator is defined to be the simplest form ? I try to understand it but I cannot.Why is $\frac{\sqrt 3}{3}$ simpler than $\frac1{\sqrt 3}$?
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Not simpler in itself but e.g. if we want to add a rational.. – Berci May 09 '18 at 16:03
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1The first one is much easier to calculate to any number of decimals than the second. – MasB May 09 '18 at 16:06
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I'm not sure how credible this is, but the way I've seen it is how rationalizing the denominator was probably used to quickly calculate certain expressions in your head.
For example, say you wanted to numerically calculate $\frac 1{\sqrt2}$ and you know that $\sqrt2\approx 1.414$. Which way would be easier, calculate $\frac 1{\sqrt2}$ or calculate $\frac {\sqrt2}2$?
Frank W
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Of course the two expressions are equivalent, one reason to prefer the first one can be motivated when we need to make calculation which involve fractions, in this case the calculation of the $\gcd$ in compact form is simpler if we deal with integer number.
user
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Simply because it's just easier to deal with, often times it's not necessary but it's still a good habit.
Class
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A general procedure in mathematics (and other fields of science) is to go from the known to the unknown, and to always interpret the unfamiliar in terms of the familiar.
A quick way to see the relative magnitude of a number in surd form is to rationalise the denominator, which helps you see what fraction of the simple form in the numerator the whole surd is. E.g., since one knows $\sqrt2\approx 1.4$, one can better have a feel for $2/\sqrt8$ in its simpler form than as it is.
Allawonder
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