How many whole numbers are between $\sqrt[3]{10}$ and $\sqrt[3]{200}$?
I need to find the range of values that $\sqrt[3]{10}$ and $\sqrt[3]{200}$ lie in. I know that $\sqrt[3]{8} = 2$ and $\sqrt[3]{27} = 3$, so $\sqrt[3]{10}$ must be between 2 and 3. Similarly, I know that $\sqrt[3]{125} = 5$ and $\sqrt[3]{216} = 6$, so $\sqrt[3]{200}$ must be between 5 and 6. Therefore, the whole numbers between $\sqrt[3]{10}$ and $\sqrt[3]{200}$ are 3, 4, and 5. There are 3 such numbers.

