4.56666

0
-25
square root of -25
square root of 42
6.263
square root of 36
9/11

natural number
whole number
integer
rational number
irrational number

The given numbers can be categorized as follows:

4.56666 - rational number
0 - whole number, integer, rational number
-25 - whole number, integer, rational number
square root of -25 - imaginary number
square root of 42 - irrational number
6.263 - rational number
square root of 36 - whole number, integer, rational number
9/11 - rational number