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May 12th, 2017, 08:59 AM   #1
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Square Root in Algebra

Marissa was given the volume of a cube-shaped chest. One of the sides can be found by taking the cube root of 2000x$\displaystyle ^3$y$\displaystyle ^1$$\displaystyle ^0$ What is the length of one side of the cube in its simplest form?

How would I begin this? Would I just find the square root of 200x$\displaystyle ^3$y$\displaystyle ^1$$\displaystyle ^0$?

Or would I find the cube root of it?

Last edited by Indigo28; May 12th, 2017 at 09:02 AM.
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May 12th, 2017, 11:06 AM   #2
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Originally Posted by Indigo28 View Post
Marissa was given the volume of a cube-shaped chest. One of the sides can be found by taking the cube root of 2000x$\displaystyle ^3$y$\displaystyle ^1$$\displaystyle ^0$ What is the length of one side of the cube in its simplest form?

How would I begin this? Would I just find the square root of 200x$\displaystyle ^3$y$\displaystyle ^1$$\displaystyle ^0$?

Or would I find the cube root of it?
Well the problem specifically states that one of the sides can be found by taking the cube root of $\displaystyle 2000x^3y^10$.

So to simply answer the question it is $\displaystyle \root 3\of{2000x^3y^{10}}$

But i think it is best to understand why the side of the cube is this.

Remember that the definition of a cube is that it is equal on all six sides and that the volume of a cube is $\displaystyle x*y*h$. So if given a volume of a cube, you cube root it to find the length of one side, and if you find one, you find all.

Looking at this volume formula though, it is hard for me to visualize how this is a cube since the volume changes at different rate depending on the value of x as oppose to y, but it could be that x and y don't represent the length of the sides in this formula. Or it is just someone someone made up quickly as a math problem without considering it to be wholly accurate.

Anyways, I hope this helps.
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May 12th, 2017, 12:02 PM   #3
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I think there is confusion between "side" and "edge" here. A cube has six sides, each one a square. It has 12 edges, each one a line segment.
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