Question

Prove that 5+3√2 is an irrarational number

Answer 1

Answer:

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Answer 2

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Let us assume , to the contrary , that 5 + 3√2 is an rational number

So ,

$\sf \mapsto 5 + 3 \sqrt{2} = \frac{a}{b} \\ \\ \sf \mapsto 3 \sqrt{2} = \frac{a}{b} - 5 \\ \\ \sf \mapsto \sqrt{2} = \frac{a - 5b}{3b}$

We get a - 5b/3b is rational , and so √2 is rational

But this contradicts the fact that √2 is irrational

So , we conclude that 5 + 3√2 is irrational