Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps.
Problem:
John is playing a game where he has to guess the weight of a giant watermelon. The watermelon weighs 729 pounds. John wants to estimate the side length of a smaller cube-shaped watermelon that would weigh the same as the giant watermelon. How long is each side of the smaller cube-shaped watermelon?
Solution:
To solve this problem, we need to find the cube root of 729.
The cube root of a number is a value that, when cubed, gives the original number. In other words, if "x" is the cube root of "y", then x³ = y.
In this case, we want to find the cube root of 729. We can express this as:
x³ = 729
To simplify this equation, we take the cube root on both sides:
∛(x³) = ∛729
This simplifies to:
x = ∛729
Now, we can evaluate the cube root of 729:
x = 9
Therefore, each side of the smaller cube-shaped watermelon is 9 inches.