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.

]]>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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