Question

6+√2 is rational or irrational​

Answer 1

6+ root 2 is an irrational number

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Answer 2

Explanation

Let us assume, to the contrary , that ( 6+ √2 ) is rational

Then , there exist co - prime a and b

where

$\rm \implies(b \not = 0)$

such that

$\rm \: (6 + \sqrt{2} ) = \dfrac{a}{b}$

$\rm \implies \sqrt{2} = \dfrac{a}{b} - 6$

$\implies \: \rm \sqrt{2} = \dfrac{a - 6b}{b}$

Since a and b are integers , so

$\rm \dfrac{a - 6b}{b} \: \: is \: \: rational \: \: number$

Thus

√2 is also rational.

But , this contradicts the fact that √2 is irrational

so , our assumption is incorrect.

Hence , ( 6 + √2 ) is irrational