Question

What is the side length of the cube with a volume of 1536 cubic inches

Answer 1

`\boxed{s=8\sqrt[3]3\ in}`

Explanation:

The formula of a volume of a cube:

`V=s^3`

s - length of edge

We have

`V=1536\ in^3`

Substitute:

`s^3=1536\to s=\sqrt[3]{1536}`

`\begin{array}c1536&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`

Use

`\sqrt[3]{a^3}=a`

and

`\sqrt[3]{ab}=\sqrt[3]{a}\cdot\sqrt[3]{b}`

`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`

Answer 2

Volume = S^3

Volume = 1536 cubic inches

1536 = s^3

Take the cubic root of each side:

S = ∛1536

Since volume is cubed ( raised to the 3rd power, rewrite 1536 using a cubed number:

1536 = 8^3 *3

Now you have S = ∛(8^3*3)

Pull terms out from under the radical to get:

Side = 8∛3