Find the greatest number of five …

The greatest 5 digit number= 99999.

First we have to find out the smallest number which should be subtracted from this number to obtain a perfect square. For this we apply the method of finding the square root of 99999 by division method.

The final remainder is 143. Hence,if we subtract 143 from 99999 then the new number will be a perfect square. Whose Square root is 316.

Hence, the required number is 99999- 143= 99856

√99856= 316

We know that the largest 5 digit number is 99999. So let us check whether it is a perfect or not ?

So here we can see that 99999 is not a perfect square as it leaves 143 as the remainder while finding it s square root.

So for finding 5 digit perfect square we will have to subtract 143 from 99999

=> 99999-143 = 99856

Hence 99856 is a perfect square whose square root is √99856 = 316.