Prove that√5 is a irrational number

The square root of five is 2.2360679775 ...

Step-by-step explanation:

The square root of five is irrational because it never ends (example: 3.1415 ...)

Answer: 1. This irrationality proof for the square root of 5 uses Fermat's method of infinite descent: Suppose that √5 is rational, and express it in lowest possible terms (i. e., as a fully reduced fraction) as mn for natural numbers m and n. Then √5 can be expressed in lower terms as 5n - 2mm - 2n, which is a contradiction.