Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps.
Problem: The volume of a cube is equal to 125 cubic units. What is the length of each side of the cube?
Solution:
Let's assume that the side length of the cube is represented by "x". The volume of a cube is given by V = x^3, where V is the volume.
Given that the volume of the cube is 125 cubic units, we can set up the equation:
x^3 = 125
To solve for x, we need to find the cube root of 125.
Taking the cube root of both sides, we get:
∛(x^3) = ∛125
Simplifying this, we have:
x = ∛125
We can evaluate this by finding the prime factors of 125, which are 5^3:
x = ∛(5^3)
Taking the cube root of 5^3, we get:
x = 5
Therefore, the length of each side of the cube is 5 units.