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#1 2011-05-18 06:00:22

reconsideryouranswer
Member
Registered: 2011-05-11
Posts: 172

Sum of radicals versus an integer

[I made up the following (or rediscovered it).]

Without estimating any square roots (but allowing repeated squaring
of sides and using the four main operations), in theory, is it possible
to work out which of the following sides is larger?




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#2 2011-05-18 11:46:34

bobbym
Administrator
From: Bumpkinland
Registered: 2009-04-12
Posts: 88,584

Re: Sum of radicals versus an integer

Hi;

First thing is to prove:

Since both sides are positive we can square without changing the inequality.

Subtract 5.

Again we can square without changing the inequality.

The second part we prove:

Since both sides are positive we can square without changing the inequality.

Subtract 12.

Square again.

So:

Add them up.


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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