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

1 Answer
Mar 7, 2016

Answer:

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.