Answer:
[tex]\boxed{s=8\sqrt[3]3\ in}[/tex]
Step-by-step explanation:
The formula of a volume of a cube:
[tex]V=s^3[/tex]
s - length of edge
We have
[tex]V=1536\ in^3[/tex]
Substitute:
[tex]s^3=1536\to s=\sqrt[3]{1536}[/tex]
[tex]\begin{array}{c|c}1536&2\\768&2\\384&2\\192&2\\96&2\\48&2\\24&2\\12&2\\6&2\\3&3\\1\end{array}\\\\1536=2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot2\cdot3=2^3\cdot2^3\cdot2^3\cdot3[/tex]
Use
[tex]\sqrt[3]{a^3}=a[/tex]
and
[tex]\sqrt[3]{ab}=\sqrt[3]{a}\cdot\sqrt[3]{b}[/tex]
[tex]s=\sqrt[3]{2^3\cdot2^3\cdot2^3\cdot3}=\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]{2^3}\cdot\sqrt[3]3\\\\=2\cdot2\cdot2\cdot\sqrt[3]3=8\sqrt[3]3\ in[/tex]
