Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps
Problem:
Maria has a garden in the shape of a cube. She wants to know the length of one side of the cube so she can plant a specific type of tree that requires a certain amount of space. The volume of her garden is 343 cubic meters. What is the length of one side of Maria's garden?
Solution:
Let's assume that the length of one side of the cube is "x". Therefore, the volume of the garden can be represented as x^3.
We are given that the volume of the garden is 343 cubic meters, so we can set up the equation as follows:
x^3 = 343
To find the length of one side, we need to take the cube root of both sides of the equation. The cube root of a number "a" can be represented as ∛a.
∛(x^3) = ∛343
Simplifying both sides, we have:
x = ∛343
Now, we can evaluate the cube root of 343:
x = ∛343
x = 7
The length of one side of Maria's garden is 7 meters.