Question

what least number must be added to 594 to make the sum a perfect square?

Answer 1

24^2 > 594 > 25^2
576 > 594 > 625

so, (625-594) 31 must be added to 594 to make it a perfect square.

Answer 2

31 is the least number to be added to make 594 a sum of perfect square .

Given:

594

To find:

The least number to be added to make 594 a sum of perfect square = ?

Solution:

To find the least number to add to 594 to make it a perfect square is by finding the nearest greater and least square number. The nearest greatest perfect square is $\left(576=24^{2}\right)$ and the nearest smaller perfect square is $\left(625=25^{2}\right).$

Now let us find the difference between 625 and 594: 625 – 594 = 31. The difference between the greatest and the nearest perfect square number is 31.

Now to reach the nearest perfect square number we have to add the least number thereby $\left(576=24^{2}\right)$ is not taken into consideration.

Hence, the least number to be added to 594 to make perfect square is 31.