It is theorem in which if we put root on any prime number then it will be irrational.

Explanation:

Definition of a Prime Number:
A prime number is a natural number greater than 1 that has no positive divisors other than 1 and itself. In other words, a prime number cannot be divided evenly by any other number except 1 and itself.

Rational Numbers:
Rational numbers are numbers that can be expressed as the quotient or fraction p/q, where p and q are integers and q is not equal to 0. In simple terms, rational numbers can be written as fractions.

Proof that p is an Irrational Number:
To prove that p is an irrational number, we need to show that p cannot be expressed as the quotient or fraction p/q, where p and q are integers and q is not equal to 0.

Assume p is a Rational Number:
Let's assume that p is a rational number. So, p can be expressed as the fraction p/q, where p and q are integers and q is not equal to 0.

Properties of Rational Numbers:
Property 1: The product of two rational numbers is also a rational number.
Property 2: The quotient of two rational numbers is also a rational number, provided the denominator is not equal to 0.

Applying Property 2:
Using Property 2, we can write the equation as p = p/q, where p and q are integers and q is not equal to 0.

Multiplying both sides by q:
Multiplying both sides of the equation by q, we get p*q = p.

Simplifying the equation:
Simplifying the equation, we have q = 1.

Contradiction:
Since q is an integer, it cannot be equal to 1. This contradiction arises from assuming that p is a rational number.

Conclusion:
Therefore, our assumption that p is a rational number is incorrect. Hence, p cannot be expressed as a fraction and is therefore an irrational number.