Calculate Work: Aquarium 2m x 1m x 1m Full of Water

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an aquarium 2 m long, 1 m wide and 1 m deep is full of water. find the work needed to pump half of the water out of the aquarium. Density of water is 1000kg/m^2

My work is in the paint doc.
 

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I added another paint doc hopefully this one is easier to readf..
 

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There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
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