Question

Prove that 6-√2 is an irrational.​

Answer 1

LET US ASSUME, to the contrary that 6-√2 Is rational.

that is, we can find coprime a and b (b≠0) such that 6-√2 = a/b .

Therefore, 6-a/b = √2

Rearranging this equation, we get

√2 = 6-a/b = 6b-a/b

°.° a and b are integers, we get 6-a/b is rational, and so √2 is rational.

But this contradicts the fact that √2 is irrational .

This contradiction has arisen because of our incorrect assumption that 6-√2 is rational.

So, WE CONCLUDE THAT 6- √2 IS IRRATIONAL.