Question

Find the greatest $4$-digit number, which is a perfect square. Find its square root.

Answer 1

The greatest $4$-digit number is $9999$.

First, find the least number which when substracted from $9999$ gives a perfect square.
$\mid 99\overline{9\mid \underset{–}{99}\underset{–}{99}}\mid -81\overline{189\mid 1899}\mid -1701\overline{\mid 198}$
The remainder is $198$. The required number, which is a perfect square is $9999-198=9801$
and clearly, $\sqrt{9801}=99$.