Question

Prove that
$\sqrt[3]{2}$
is an irrational number.

Answer 1

Hey !!!

Let us assume , to. contrary , that 3√2 is rational .

that is we can find coprime a and b (b is not equal to 0 ) such that 3√2 = a/b

REARRANGING , we get √2 = a/3b

since 3 , and b are integer a/3b is rational ,.and √2 is rational .

but this contracticts the fact that √2 is rational and so ,

we conclude that 3√2 is irational no.

hope it helps you !!!

@Rajukumar111