solve (-9 - sqrt108)/3?

Question

(-9 - sqrt108)/3

I think the answer is -3 * -2sqrt27 or am I way off.

Answer 1

(-9-sq.rt108)/3
=-9-6rt3/3
=-3-2rt3

Answer 2

I get -3 - 2*sqrt3

I'd break this up first into -9/3 - (sqrt108)/3

the first term simplifies to -3, so factor 108 under the sqrt to see what you can pull out:

-3 - (sqrt[2*2*3*3*3])/3

For every "double" factor, you can pull one outside of the sqrt and remove both from the inside, so now you have:

-3 - (2*3sqrt[3])/3

simplify further to take a factor of 3 out of the top and bottom of your fraction and you end with:

-3 - 2*sqrt3

I'm guessing you tried to simplify the 3 on the bottom of the original problem by only removing it from the 9 on top. Since the problem starts with a sum (well, difference in this case) you have to keep the 3 as the denominator for both terms. And, you didn't get the factor of 9 in 27 pulled out from under the sqrt. Always use prime factorization for these types of simplification and you'll easily see what to remove from the sqrt (remove pairs within the sqrt to let you move a single factor outside of the sqrt). If you just look for squares (like 4 or 9) you might miss something as you did here. Good luck

Answer 3

No, recall that the 3 is dividing the sqrt too

(sqrt 108)/3 = [sqrt (4 * 27)]/3 = sqrt 4*sqrt (27/9) = 2 sqrt 3

So, the answer is -3 - 2 sqrt 3 or the one that Doug already told you.

Ana

Answer 4

You're off, but only by a little ☺
It's -3 - (2/3)√27


Doug

Answer 5

sqrt(108)= 6sqrt(3) so the answer is -2sqrt(3) -3