My stupid math teacher...

[gaelic cowboy]

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

[Tellos Athenaios]

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).

[gaelic cowboy]

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.

[Tellos Athenaios]

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

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

[gaelic cowboy]

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

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

[Prussian to the Iron]

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.