Question

Prove that of the numbers `sqrt (6) ` is irrational:

Answer 1

Let `sqrt(6)  = sqrt(2) × sqrt(3)` be rational.
Hence, `sqrt(2) ,  sqrt(3)` are both rational.
This contradicts the fact that  `sqrt( 2) ,   sqrt(3 )`  are irrational.
The contradiction arises by assuming `sqrt(6)` is rational.
Hence, `sqrt(6)` is irrational.