The square root of 25 is 5, which 

1. A rational number, since 5 is the ratio of the two integers 5 and 1.
2. An integer since 5 is an element of {...,-3,-2,-1,0,1,2,3,...} 
3. A whole number, since 5 is an element of {0,1,2,3,...}
4. A counting number, since 5 is an element of {1,2,3,...}

The square root of 5 is only 

1. An irrational number, since it is not the ratio of any two integers.

[It can only be approximated by
this nonrepeating infinite decimal, it goes on forever:

2.2360679774997896964091736687312762354406183596115257...]

Edwin