Question

Is 12√2 is an irrational number ? Why

Answer 1

Answer:

Yes, 12√2 is an irrational no.

Step-by-step explanation:

let us assume to the contrary that 12√2 is rational,then

12√2=a/b

reducing a and b to their lowest form,

12√2=p/q (where p and q are coprime)

By cross-multiplication,

√2=p/12q -(1)

(1) shows that √2 can be expressed in the form of c/d and therefore it is a rational no.

But we know that √2 is irrational.

This contradiction arises because of our false assumption that 12√2 is rational

Hence 12√2 is an irrational no. .

Hope it helps!