A cube has a volume of 1280 cubic feet. Determine the edge length of the cube as a radical in simplest form.
cuberoot(1280)
cuberoot(64 * 20)
4 * cuberoot(20)
To find the edge length of the cube, we need to find the cube root of the volume.
Let's find the cube root of 1280:
∛1280 ≈ 10
Therefore, the edge length of the cube is 10 feet.
To determine the edge length of a cube, we can use the formula for the volume of a cube:
Volume = side length^3
Given that the volume of the cube is 1280 cubic feet, we can set up the equation as follows:
1280 = side length^3
To find the side length, we need to take the cube root of 1280. In simplest radical form, we can write it as:
side length = ∛1280
To find the cube root of 1280, we can use a calculator or simplified it manually as follows:
1280 = 2^7 * 5
To simplify the cube root:
∛(2^7 * 5) = ∛2^6 * ∛2 * ∛5
Since ∛2^6 = 2^2 and ∛2 = 2, we can simplify further:
side length = 2^2 * 2 * ∛5
= 4 * 2 * ∛5
= 8∛5
Therefore, the edge length of the cube, in simplest radical form, is 8∛5.