How to prove that π is an irrational number

How to prove that π is an irrational number

This problem was first proved by the German mathematician Lambert in the 17th century. His proof was written by Tan (m/n) in the form of a complex fraction. If m/n is a rational number, the term of the complex fraction is infinite, but according to the nature of the complex fraction, a complex fraction whose term is infinite represents an irrational number.

How to prove that the three numbers are irrational? 5^(1/3)-3^(1/3) Ln2 2^(2^(1/2))

1. Suppose that 5^(1/3)-3^(1/3) is a rational number, then there is an integer m, n such that 5^(1/3)-3^(1/3)= m/n 5^(1/3)= m/n +3^(1/3)= m/n +3^(1/3) Both sides of the equation cube 5= m^3/n +3+3* m^2/n *3^(1/3)+3* m/n *3^(2/3) Finishing 2-m^3/n ^3=3* m^2/n *2*3^(1/3)+3* m/n *...