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

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

bobbym
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: