Question

describe how to construct a cube that could be used to determine the cube root 729.

Answer 1

Solution:

We can construct a cube with the given volume:

$V=729in^3$

now, to build it we must know the length of each side of the faces of the cube. Let us denote by z this length. According to the above equation, we get:

$V=729in^3=z\mathrm{}z\mathrm{}z=z^3$

This is equivalent to saying:

$z^3=729$

to find the length of the side z, so we can construct the cube with volume 729, we must apply cube root to the previous equation:

$z^{}=\sqrt[3]{729}\text{ = 9}$

then

$z\text{ = 9}$

so we can construct a cube such that each of its sides has a length of z=9 = the cube root of 729.