Question

Prove 1/3root2 to be an irrational number

Answer 1

suppose 1/3√2 = rational no

by dividing its common factor

1/3√2 = a/b

b=3√2a

b/3a= √2

b,a, 3 are integers

which implies b/3a is rational no

which also implies √2 is also rational

this contradicts the fact that √2 is irrational

hence, 1/3√2 is irrational no

prooved