Question

prove that n√p is irrational number, where p is a positive non perfect square number

Answer 1

Hey ✌

Let us assume that n√p is a rational number,
Than,

=> n√p = a/b (where a and b are co-prime)
=> √p = a/b x 1/n is rational number
=> √p = a/bn is rational number

But it contradict the fact that √p is an irrational number as p is a positive non perfect square number.

So, a/bn is also an irrational number.

Hence, our assumption is wrong n√p is an irrational number.

Hence Proved
Thank you