Question

Prove tahat 3-root 2 is an irrational

Answer 1

GIVEN : $3 \sqrt{2}$ a number.

PROVE : We have to prove that $3 \sqrt{2}$ is an irrational number.

PROOF :

• Let us assume that $3 \sqrt{2}$ is a rational number.

=> $3 \sqrt{2}$ = $\bigg( \dfrac{a}{b}\bigg)$

Here.. 'a' and 'b' are co-prime numbers.

=> $\sqrt{2}$ = $\bigg( \dfrac{a}{b}\:-\:3\bigg)$

=> $\sqrt{2}$ = $\bigg( \dfrac{a\:-\:3b}{b}\bigg)$

Here..

$\bigg( \dfrac{a\:-\:3b}{b}\bigg)$ is a rational number. So, $\sqrt{2}$ is also a rational number.

But we know that $\sqrt{2}$ is irrational number.

Means, our assumption is wrong.

$3 \sqrt{2}$ is an irrational number.

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