Question

Prove that for any positive integer p, √p is irrational no.

Answer 1

Any number of the form p/q where p and q are integers is said to be a rational number

for a prime number say 29 the simplest form the square root will be

now this cannot be represented in the rational number form as

is not an integer

so any prime number has only 1 and the number itself as factors and hence the square root cannot be an integer.

Hence it cannot be represented in the rational number form of p/q where both p and q should be integers.

This holds true for every prime number