is 5.66… rational or irrational

The number 5.66... is rational.

is the square root of 81 rational or irrational

The square root of 81 is rational. It is equal to 9, which is a whole number, and all whole numbers are rational.

is negative seven thirds rational or irrational

Negative seven-thirds (-7/3) is a rational number. It can be expressed as a fraction, where both the numerator and denominator are integers, and the denominator is not zero.

is 2 a rational or irrational number

The number 2 is a rational number. It can be expressed as the fraction 2/1, where both the numerator and denominator are integers and the denominator is not zero.

put these in order from rational to irrational:

0.566…
square root of 81
(-7/3)
2
square root of 8
pi
19

In order from rational to irrational:

(-7/3)
2
19
0.566...
√8
√81 (9)
π (pi)

which of the numbers are rational