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

1 Answer
Mar 7, 2016

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.