How many positive whole numbers have cube roots that are less than $10$? For example, $20$ would count since $\sqrt[3]{20}<10.$
I need to find the largest positive whole number $n$ such that $\sqrt[3]{n}<10$. If I cube both sides of the inequality, I get $n<10^3=1000$. So, any positive whole number less than $1000$ has a cube root that is less than $10$. There are $999$ such numbers, since I can count them from $1$ to $999$. 