Is the square root of 5 an irrational or a rational number?

Answer 1

A rational number can be expressed as the ratio of two integers (the number one does not count). An irrational number cannot.

The square root of 5 cannot be expressed as the quotient of two integers. This assertion is by experience that the square root of a Prime number is irrational. There are several methods to prove the irrationality -- look for them elsewhere.

For the sake of curiosity, my calculator gives the following result for it:

2.2360679774997896964091736687312762354406183596115257242708972454105209256378048994144144083787822749695081761507737835042532677244470738635863601215334527088667781731918791658112766453226398565805357613504175337850034233924140644420864325390972525926272288762995174024406816117759089094984923713907297288984820886415426898940991316935770197486788844250897541329561831769214999774248015304341150359576683325124988151781394080005624208552435422355561063063428202340933319829339597463522712013417496142026359047379...

You can say that it is irrational by looking at the inexact answer.