To answer this question, we need to define what a rational and irrational number means
A rational number is a number that can be expressed as a ratio of two integers where both the numerator and the denominator in the fraction are integers.
To check if the options are rational or irrational numbers
Step 1: Find the square root of the numbers
[tex]\sqrt[]{12}\text{ =}2\sqrt[]{3}[/tex]
since 2√3 cannot be expressed as a ratio of two integers, then It is not a rational number
[tex]-\sqrt[]{81}=-9[/tex]
since -9 can be expressed as a fraction:
[tex]-9=-\frac{9}{1}[/tex]
It is a rational number