Prove that the following is irrational: 6+√2

Let 6 + √2 be rational.
Therefore, we can find two co-prime integers a, b (b 0) such that
6 + √2 = a/b
⇒ √2 = a/b – 6
Since a and b are integers,a/b – 6 is also rational and hence, √2 should be rational. This
contradicts the fact that √2 is irrational. Therefore, our assumption is false and hence,
6 + √2 is irrational.

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