Question

Prove that of the numbers  `3 sqrt(7)`  is irrational:

Answer 1

Let `3 sqrt(7)` be rational.
`1/3 ×3 sqrt(7)= sqrt(7)` = rational          [∵Product of two rational is rational]
This contradicts the fact that `sqrt(7)` is irrational.
The contradiction arises by assuming `3 sqrt(7)` is rational.
Hence, `3 sqrt(7)` is irrational.