Question

Prove that 6+ root 2 is irrational

Answer 1

Here Is Your Ans ⤵

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Let , 6 + √2 is an rational number

➡ 6 + √2 = A / B

➡√2 = A / B - 6

Integer = Fraction

So , Our assumptions is Wrong

6 + √2 is an irrational number

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Answer 2

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=>Let assume that 6+√2 is a rational no.

Hence,

$6 + \sqrt{2} = \frac{a}{b}$

(Here a and b are coprime)

$\sqrt{2 } = \frac{a}{b} - 6$

$= > \sqrt{2} = \frac{a - 6b}{b}$

=>Now, a-6b/b is a rational no.

=>Hence,√2 is also a rational no.

=>But this contradicts the fact

=>Our assumption is wrong.

Hence,6+√2 is an irrational no.

Hope it helps...