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reconsideryouranswer

Member

Registered: 2011-05-11

Posts: 171

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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bumpkin

From: Bumpkinland

Registered: 2009-04-12

Posts: 109,606

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.

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In mathematics, you don't understand things. You just get used to them.
If it ain't broke, fix it until it is.
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