Question

Given that √2 is rational.prove that 5+3√2 is irrational number​

Answer 1

once touch the answer please

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Answer 2

Step-by-step explanation:

let us assume that (5+3√2) is rational.

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

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

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

Because ‘a’ and ‘b’ are integers a−5b/3b is rational

3b is rational. That contradicts the fact that √2 is irrational.The contradiction is because of the incorrect assumption that (5 + 3√2) is rational.So, 5 + 3√2 is irrational.