Question

How do you simplify `(-9-sqrt108) / 3`?

Answer 1

By reducing the radical and dividing by three.

Explanation:

In the problem, you have `sqrt(108)` which we can reduce from using a factor tree.

If you look up how to do it there will be a multitude of examples for you to look at, but it's really hard to format it here.

108 = 542 = 2722 = 9322 = 33322. We can take out a pair of two's and three's which gives us our simplified radial `6sqrt(3)`.

That simplified radical gives us the problem `(-9-6sqrt(3))/3`.

Now we can factor out three's from `9` and `6sqrt(3)` and divide the three's out by the three in the denominator, which gives us a simplified `-3-2sqrt(3)` which should be your final answer.