I need help with this problem. -9 minus square root of 108 divided by 3?

Question

I am getting confused by this problem and really need an explaination of how to work this one out. please will someone help me?

Answer 1

The big question is whether it is sqrt(108) / 3 or sqrt(108/3)...

Assuming it is the 2nd case (because it comes out evenly) you have:

-9 - sqrt(108/3)
-9 - sqrt(36)

Now there are two answers, because sqrt(36) = ±6.
-9 - 6 = -15
-9 - (-6) = -9 + 6 = -3

The answers are -3 or -15. If your teacher only expects you to give positive square roots, then the answer is:
-9 - 6
-15

Answer 2

Follow order of operations:

First take the square root of 108. Since 36 is a factor of 108 and 36 is also a perfect square, it simplifies to 6 times the square root of 3. You now have -9 - (6 times sq. rt. of 3) divided by 3. Order of operations next says to perform division before subtraction. So divide 6 by 3 (sq. rt. of 3 doesnt change). Youre left with -9 minus (square root of 3). That is an exact answer. If you need an approximate answer, evaluate the sq rt of 3 and subtract it from -9.

Answer 3

ok. The cool ingredient about roots and fractions is that you do not choose decimals to figure them out First, are you positive there is no longer a typo and it truly is sixty 4/9? That'd be a lot less annoying. besides, the dice root of fifty 4/9 is only the dice root of one decision over the dice root of the different. So it will be (dice root of fifty 4)/3 Now seem at the different section. The sq. root of 1296 is 36. Your calculator will allow you to keep in mind that. So at present you've (dice root of fifty 4)/3 - 3(sqrt(1296)) Which simplifies to (dice root of fifty 4)/3 - 3(36) which inserts right down to (dice root of fifty 4)/3 - 108 wish it truly is sensible!

Answer 4

Well, there are three ways to interpret your statement of the problem:

a) [-9 - sqrt(108)]/3 ==> = -3 - sqrt(108)/3 = -3 - sqrt(9*4*3)/3 = -3 - 3*sqrt(4*3)/3 = -3 - 2sqrt(3) (use a calculator if you need)

b) -9 - sqrt(108/3) ==> -9 - sqrt(36) = -9 - 6 = -15

c) -9 - sqrt(108)/3 = -9 - sqrt(9*4*3)/3 = -9 - 6sqrt(3)/3 = -9 -2sqrt(3)

Answer 5

Please type the expression in numerical data, including the square root and division sign, and use parenthesis.
Did you mean: (- 9 - V`108) / 3 Or, - 9 - [(V108)/3]?

I'll solve both equations.

1. (- 9 - V`108) / 3
First: find the square root of 108 - express 108 in lowest terms...

(- 9 - V`4*27) / 3

(- 9 - V`2*2*3*3*3) / 3

(- 9 - (2*3)V`3) / 3

(- 9 - 6V`3) / 3

(- 9/3) - (6/3V`3)

(- 3) - (6/3V`3) = - 3 - 2V`3


2. - 9 - [(V108) / 3]
First: express 108 in lowest terms...

- 9 - [(V2*2*3*3*3) / 3]

- 9 - [(V2*2*3*3*3) / 3]

- 9 - [2*3(V3) / 3]


- 9 - (6V3)/3

- 9 - 2V`3

Answer 6

1. First, take the square root of 108.
2. Once you get that number, it will be between 10 and 11, divide it by 3.
3. Take that number, it should be around +3 something, and subtract it from negative nine. This should give you around negative 12 something. (-9-3something = -12 something).
4. You can use a calculator if you like.

Answer 7

Try writing it out exactly as you read it.

-9 - SQRT(108)/3

simplify using standard math order rules
* / + -

"Puzzlings" answer makes sense so i suspect he/she has the correct answer. It is not as if the school is going to give you questions that require you to come up with decimal place accuracy unless they say answer to 3 decimal places or words to that effect.