Write a word problem whose solution involves taking a cube root. State the problem and solve it, showing and explaining all steps.

Answer 1

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.