Question

Show that $3\sqrt{2}$ is irrational

Answer 1

Step-by-step explanation:

Let if possible let 3√2 be rational.

Then,3√2 is rational,1/3 is rational

=1/3*3√2(Product of two rationals is rational)

=√2 is rational

This contradicts the fact that √2 is irrational.

The contradiction arrises by assuming that 3√2 is rational .

hence,3√2 is irrational.

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Answer 2

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ATQ,

$let \: us \: assume \: that \: 3\sqrt{2} \: is \: rational \: \\ and \\ 3\sqrt{2} = \frac{a}{3b} \\ now \\ a \: and \: b \: and \: 3 \: are \: integers \: \\ so \: they \: are \: rational \: and \: \sqrt{2} \: is \: also \: rational \\ but \: this \: contradicts \: the \: fact \: that \: \sqrt{2} \: is \: irrational \: \\ hence \: 3\sqrt{2} \: is \: irrational$

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