How many natural numbers strictly between $81$ and $100$ are NOT perfect squares?

How many natural numbers strictly between $81$ and $100$ are NOT perfect squares?
  1. $18$
  2. $17$
  3. $19$
  4. $20$

Solution

Numbers strictly between $81$ and $100$ are $82, 83, \ldots, 99$, i.e., $18$ numbers. None of them is a perfect square (since $9^{2} = 81$ and $10^{2} = 100$ are at the boundary, both excluded).

Asked in: IMO

Practice more SQUARES AND SQUARE ROOTS questions on Aicharya