It is an irrational no. because it cannot be expressed in the form of p/q

Proof that 2√3 is an irrational number:
1. Assume that 2√3 is a rational number:
- Let's assume that 2√3 is a rational number, which means it can be expressed as a fraction where both the numerator and denominator are integers and the denominator is not zero.
2. Express 2√3 as a fraction:
- We can write 2√3 as a fraction in the form of a/b, where a and b are integers with no common factors other than 1.
3. Square both sides:
- Squaring both sides of the equation 2√3 = a/b, we get 12 = a^2/b^2.
4. Conclude that √3 is irrational:
- Since 12 is not a perfect square and cannot be expressed as the ratio of two integers, we can conclude that √3 is irrational.
5. Contradiction:
- This contradicts our assumption that 2√3 is a rational number. Therefore, we can say that 2√3 is an irrational number.
In conclusion, by assuming that 2√3 is a rational number and following the logical steps outlined above, we have proved that 2√3 is indeed an irrational number.