My stupid math teacher...

Alright, so on a worksheet today, she worked out a simple math problem. Or so she thought. Upon closer inspection, her answer is completely wrong, in addition to the question not having any sort of non-decimal answer.

The Question:

Given: 6 times (X^2)=36
X^3=?

Her answer:

X^3=3 times cubed root of 8

Her answer is obviously wrong. first off, cubed root of 8 is 2. no matter, it comes out to 6 either way.
second, if you take the cubed root of 6 (in order to get X to the 1st power), it comes out to 1.81712059. This squared, to come out with X squared (as in the first part of the problem), multiplied by 6, does NOT come out to 36.
in fact, nothing squared times 6 equals 36 (except, obviously, the square root of 6, rather than the CUBED root)

Perhaps I'm missing something, but if anyone works this out and finds that it does in fact come out as X cubed equals 6, but at the same time X squared times 6 equals 36, please tell me how, because apparently I'm lost.

I know I'm right, I just want to see if I missed something.

This has to be a mistake teacher probably meant to write X^2 not X^3 unless you left some of the question out???

answer is X^2=6 for me anyway and if they are really looking for X^3 then the answer is 6 x (sqrroot6)

But my money is on a simple mistake in writing the question and that it is supposed to be X^2

As stated, there are two solutions to the problem. First of all x² = 36/6 (hence x² = 6), has two solutions: x= sqrt(6), or x = - sqrt(6). As a result x³ = - (6^(3/2)), or x³ = 6^(3/2).

But we can simplify the answers above for 6 = 3 *2.
So 6^(3/2) = (3^(3/2)) * (2 ^(3/2)) = 3*sqrt(3) * 2*sqrt(2) = sqrt(27) * sqrt(8) = sqrt(216). (Through various identities on powers.)
EDIT: Plug these simplifications in the answer:
x³ = sqrt(216), or x³ = - sqrt(216).

EDIT2: The simplification is mainly to show that the 8 your teacher got might not be a random figure pulled out of the air, we can see there is a sqrt(8) component to the answer too. Of course if you're good with the arithmetic it's faster to write 6^(3/2) = sqrt(6^3) = sqrt(216).

http://www.xamuel.com/plus-or-minus-square-roots/


Oh just on a side note Prussian Iron in case your confused 6 * (sqrt6) is the same as sqrt(216)

Tellos makes a good point about positive and negative roots myself included we can tend to disregard them.

Quote:

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Originally Posted by gaelic cowboy

http://www.xamuel.com/plus-or-minus-square-roots/

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There are two solutions to x²=y, cowboy, not two answers to sqrt(x). ~;)

Quote:

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Originally Posted by Tellos Athenaios

There are two solutions to x²=y, cowboy, not two answers to sqrt(x). ~;)

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Indeed ~:) at least not yet

now that I have looked at that sum again I'm beginging to think the X^2 is the wrong part and the first part should read instead

6 * (X^3) = 36

cos then

X^3 = 6

which is the same as 3 times cubed root of 8

I would think it was a simple mistake if she hadn't cotinued to argue it. in the 10 minutes spent discussing it, she never once said anything about maybe mistakenly putting the wrong question in, despite my repeated attempts to convince her that it was not possible for both to be true (X^3=6, and 6 X^2=36)

the way cubed root of 8 came out was because she was factoring....36? I think. either way you do it it comes out as that cannot be right.

Quote:

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Originally Posted by Prussian Iron

Alright, so on a worksheet today, she worked out a simple math problem. Or so she thought. Upon closer inspection, her answer is completely wrong, in addition to the question not having any sort of non-decimal answer.

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This is not important. The important thing is how hot she is. So, how hot is she?

Quote:

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Originally Posted by Megas Methuselah

This is not important. The important thing is how hot she is. So, how hot is she?

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Ugly, short, fat black woman........so a 1 at most. most certainly NOT a TILF.

For 3 straight years in HS I had the same crap maths teacher. He would spend the first 5 minutes of class memorising the example in the book, and would then proceed to reproduce the example exactly on the board. Mistakes and all. One year we had a guy who actually had some idea what was going on, and he asked the teacher all manner of questions which he had no idea about.

Most of the math teachers at my school are annoying at best. One for example, would produce nothing but fear in the class and even in any teacher in proximity, constantly getting neigh on everything wrong, and (via her manipulation and employment of death-stares) manage to prove herself right every time.

I feel stupid and I'm not even a math-teacher