Find the greatest five-digit number, which is a perfect square.


Given :

The given statement is 'the greatest five-digit number which is a perfect square'.

To do :

We have to find such a number.

Solution :

The greatest 5 digit number is 99999.

To find the largest 5 digit number which is a perfect square, 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.

3

3

99999

9

61

  1

   99

   61   

626

     6

   3899

   3756

      143

The remainder is 143.

Therefore, if we subtract 143 from 99999 then the new number will be a perfect square.

The required number is $99999 - 143 = 99856$.

Therefore, the greatest five-digit perfect square number is 99856.

Updated on: 10-Oct-2022

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