Question

Prove that of the numbers  `3 + sqrt (2)`  is irrational:

Answer 1

Let `3 + sqrt (2)` be rational.
Hence, 3 and `3 + sqrt (2)` are rational.
∴ `3 + sqrt (2)` – `3=sqrt (2)` = rational [∵Difference of two rational is rational]
This contradicts the fact that `sqrt (2)` is irrational.
The contradiction arises by assuming `3 + sqrt (2)` is rational.
Hence, `3 + sqrt (2)` is irrational.