Question

Show that `4sqrt2` is an irrational number. 

Answer 1

Let us assume that `4sqrt2` is a rational number.

`=> 4 sqrt2 = p/q`, where p and q are the integers and q ≠ 0.

`=> sqrt 2 = p/(4q)`

Since, p,q and 4 are integers. So, `p/(4q)` is a rational number.

But this contradicts the fact that `sqrt 2` is an irrational number.

This contradiction has arisen due to the wrong assumption that `4 sqrt 2`  is a rational number.

Hence, `4 sqrt 2` is an irrational number.