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
![\sqrt[]{12}\text{ =}2\sqrt[]{3}](https://img.qammunity.org/2023/formulas/mathematics/college/ini17we14itbwbu9ubai5pjzwu430jwn9q.png)
since 2√3 cannot be expressed as a ratio of two integers, then It is not a rational number
![-\sqrt[]{81}=-9](https://img.qammunity.org/2023/formulas/mathematics/college/rvgx33cgw7xxgz4dustcwduu6c00w3ynvg.png)
since -9 can be expressed as a fraction:

It is a rational number