As we know that the largest 3 digit number is 999. So we will find out the square root of 999 by long division method and check whether it is a perfect square or not.
It can see that 999 is not a perfect square as it leaves 38 as remainder.
So if we add 38 to 999 then it will be a 4 digit number. Therefore we will subtract 38 from 999.
999 - 38 = 961.
Hence 961 is the largest 3 digit perfect square whose square root is 31.
