Question

The greatest $6-$digit number which is a perfect square is
.

Answer 1

To find:
Greatest $6$-digit perfect square number

We know that the greatest $6$-digit number $=999,999$

Now, we try to find a square root of $999,999$ by long division method.

While calculating the square root of $999,999$ using long division method, we get the remainder as $1,998$. Hence, $999,999$ is not a perfect square number.

But on subtracting $1,998$ from $999,999,$ we will get a perfect square.

$\therefore \underset{–}{999,999-1,998=998,001}$ is the greatest $6$-digit perfect square number.

And, $998,001={999}^2$