- Product rule of radicals: √ab = √a × √b
So firstly, we have to simplify the radicals. Using the product rule of radicals, simplify these radicals as such:
4√27 = 4 × √9 × √3 = 4 × 3 × √3 = 12√3
6√75 = 6 × √5 × √15 = 6 × √5 × √5 × √3 = 6 × 5 × √3 = 30√3
Now, add these two simplified radicals as such:
12√3 + 30√3 = 42√3
42√3 is your final answer.