Task A-1.1. (4 points)

How many squares of natural numbers are there between $4^{9}$ and $9^{4}$, not including these two numbers?
## Solution.

Notice that $4^{9}=2^{18}=512^{2}, 9^{4}=3^{8}=81^{2}$. 1 point

Therefore, among the given numbers, there are squares of all numbers from 82 to 511. 1 point

Thus, the number of squares between $9^{4}$ and $4^{9}$ is $512-81-1=430$. 2 points