Question

prove that 3 under root 7 is not a rational number

Answer 1

Let 3√7 be a rational number
That is, we can find coprime a and b (b≠0) such that 3√7=a/b
Therefore, √7 = a/3b
We know that √7 is irrational no. And a/3b is integer/integer = rational no.
That give,
Irrational = rational (which is not possible)
Therefore, our supposition is wrong 3√7 is not rational. It is irrational.
Hence, Proved!!