Question

Prove that 5+3√2 is an irrational 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 rational number

So ,

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

(a - 5b)/3b is rational and so is √2 ,

But this contradicts the fact that √2 Is irrational , So we conclude that 5 + 3√2 is an irrational number

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