Question: How many natural numbers less than or equal to 1 million are either squares or cubes of natural numbers?
My Thoughts: I'm having trouble understanding the "intersection" component. I think that we're trying to determine the number of $k \in \mathbb{N}$, $k \leq 1,000,000$, such that $k = a^2$ and $k=b^3$ for some $a,b \in \mathbb{N}$. But the solutions I've seen simply note that $1,000,000 = 10^6$, so there are 10 naturals $c$ such that $c^6 = (c^2)^3 = (c^3)^2 \leq 10^6$.
I don't see how these definitions of the intersection are compatible. How is "the number of naturals that are both the square of some natural number and the cube of some natural number" the same as "the number of naturals that are the cube of the square of some natural number"?