There are a few ways to approach this.
The way that you do not want to do it is you do not want to start by multplying the radicals together. That only works with positive numbers under radicals.
Instead you want to split the negatives from the numbers under the radicals:
![√(-8)\cdot√(-27) = √(-1)\cdot √(8)\cdot√(-1) \cdot √(27)](https://img.qammunity.org/2022/formulas/mathematics/high-school/fbzsrifj7y7rb08blpsg50efj5cezr4hxt.png)
This becomes
or
.
and
,
making your answer
![-6√(6)](https://img.qammunity.org/2022/formulas/mathematics/high-school/vu0dkirj2c8m9qyyuui1cqzrtvumr2avr9.png)