Question

Prove that 6+√2 is irrational​

Answer 1

Answer:

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Answer 2

$\colorbox{red} {\colorbox{aqua} {To Prove :- }}$

6+√2 is irrational

$\colorbox{blue}{\colorbox{grey}{Solution:-}}$

Let us assume 6+√2 is rational. Then it can be expressed in the form p/q , where p and q are co-prime.

Then, 6+√2= p/q

= √2 = p/q – 6

= √2 = p – 6q / q -----(p,q,−6 are integers)

p – 6q / q is rational .

But, 2 is irrational.

This contradiction is due to our incorrect assumption that 6+ 2 is rational

Hence, 6+ 2 is irrational.

$\huge \underline \orange{Thank} \underline {\red \: { you}}$