Question

what should be added to 2582415 to make the sum a perfect square

Answer 1

We select a number to divide 2582415 such that the quotient it gives has a square near to the given number.

Consider 1606

When we divide 2582415 by 1606 we get quotient as 1607 and remainder of 1573

1607² = 2582449 which is the closest number to the given number and has a natural square root.

 2582449 - 2582415 = 34

Thus 34 needs to be added to 2582415  to make it a complete square

Answer 2

Solution :-

To find the number to be added to 2582415 to make the sum a perfect square, first we have to calculate the square root of 2582415 by long division method.

Square root of 2582415 -

                1606
            _____________
      1    | 2582415
      1    | 1 
            |----------
     26   | 158
       6   | 156  
            |_________
   3206 |     22415
         6 |     19236
            |__________
            |       3179
            |
Hence, the remainder 3179

So, (1606)² = < 2582415

The next perfect square is (1607)² = 2582449 >2582415

So, the number is to be added to

2582449 - 2582415 = 34

Therefore, 34 should be added to 2582415 to make the sum a perfect square.

Answer.