What's the point of having a rational denominator?

Question

parthkohli · Answer

My reasoning is that it is easier and much more natural.  sqrt(2) by 2 is easier to think about than 1 by sqrt(2) is.

***[isuru]*** · Answer

they have discussed the same matter here .. http://www.physicsforums.com/showthread.php?t=130776

kainui · Answer

$$\frac{ d }{ dx} \sqrt{1+x^2} $$ Just out of curiosity what is that equal to?

parthkohli · Answer

Chain Rule, probably?

kainui · Answer

$$\frac{ x }{ \sqrt{1+x^2}}$$ or $$\frac{ x \sqrt{1+x^2} }{ 1+x^2 }$$

kainui · Answer

What's easier to think about and why?

parthkohli · Answer

Both of them are simple.  But rationalizing the denominator became a thing just like writing a polynomial with highest degree first did.

tkhunny · Answer

Personal Opinion?  No point, whatsoever.  It is a convention ONLY.

The more important consideration is precision and calculation error.  For example, subtraction of numbers of nearly the same magnitude tends to result in loss of significant digits, whether the subtraction is in the numerator or the denominator.  A transformation to a related addition solves this problem.

Another more important consideration is ease of use.  Oftentimes, one form or the other is more convenient or more instructive.  There is NOT one way that is always best or simplest.

One should become proficient at manipulating symbolic expressions.  The odd act of "rationalizing" is good practice, I suppose.