Question

prove that 3root2 is an irrational number​

Answer 1

Answer:

Step-by-step explanation:

let us assume , to the contrary , that 3√2 is rational

this is , we can find coprime a and b ( b ≠ 0 ) uch that 3√2 = $\frac{a}{b}$

rearranging, we get √2 = $\frac{a}{3b}$

since 3, a and b are integers, $\frac{a}{3b}$ is rational , and so √2 is rational.

but this contradicts the fact that √2 is irrational

so, we conclude that 3√2 is irrational.