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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,552

I was recently emailed by a teacher that I had an Irrational Denominator on one of my pages. I amended it so that students would not get into trouble.

Just a throwback from the past? What do you guys think?

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,599

Hi;

Both forms are obviously correct although the rationalized denominator is slightly more stable numerically. I would think they should only take points off for the first form if the question states rationalize the denominator.

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**Alex23****Member**- Registered: 2012-01-31
- Posts: 19

Yes, the latter is more elegant.

Bobbym what do you mean by stable numerically?

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 90,599

Hi Alex23;

Slightly larger denominator. Multiplication tends to smear out significant digits and division by large numbers does not. One is an error amplifier(multiplication) and one is an error reducer. This is only a very rough definition but it is how I understand it. Division by a bigger constant is slightly better,

**In mathematics, you don't understand things. You just get used to them.**

**I agree with you regarding the satisfaction and importance of actually computing some numbers. I can't tell you how often I see time and money wasted because someone didn't bother to run the numbers.**

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**bob bundy****Moderator**- Registered: 2010-06-20
- Posts: 6,531

hi MathsIsFun,

When I was young we had to do all our calculations long hand or by use of log tables. (computers were still steam driven in those days and each one filled a building!)

So it made sense to rationalise denominators. We were also made to learn that

√ 2 ≈ 1.414

√ 3 ≈ 1.732

√ 5 ≈ 2.236

It's surprising how many calculations could be done with just that.

But now we have calculators. Does it matter any longer? I think like bobbym, only if the question says you must rationalise. Or rationalize. ( depending on where you are in the world :-) )

Bob

You cannot teach a man anything; you can only help him find it within himself..........Galileo Galilei

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**anonimnystefy****Real Member**- From: The Foundation
- Registered: 2011-05-23
- Posts: 15,657

hi bob

or "racionalisati"

Here lies the reader who will never open this book. He is forever dead.

Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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**MathsIsFun****Administrator**- Registered: 2005-01-21
- Posts: 7,552

Thanks everyone.

"The physicists defer only to mathematicians, and the mathematicians defer only to God ..." - Leon M. Lederman

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