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

Answer 1

By reducing the radical and dividing by three.

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.
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Answer 2

To simplify the expression (-9 - √108) / 3, we can first simplify the square root of 108. The square root of 108 is equal to 6√3. Therefore, the expression becomes (-9 - 6√3) / 3. To simplify further, we can divide each term by 3, resulting in -3 - 2√3.

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Answer from HIX Tutor

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

When evaluating a one-sided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.

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