Prove √6-√2 > 1 Without Estimating √6 or √2

Exercise In Logic

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We can obviously use a calculator (or Google) to check that √6-√2 > 1 since √6=2.4494…. and √2=1.4142…, but how could we prove such an inequality without checking these values?

One tool available to mathematicians is ‘a proof by contradiction’. Here we assume the opposite statement (in this case √6-√2 ≤ 1) and try to arrive at some…