Question

19. What least number must be added to 594 to make the sum a perfect square ?
20. What would be added to 7912 to make the sum a perfect square ?
21. Find the least number of six digits which is a perfect square.​

Answer 1

Answer:

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

Least number to make 7912 perfect square is 9

The least number with six digits is 100000. To find the least square number with six digits, we must find the smallest number that must be added to 100000 in order to make a perfect square. For that, we have to find the square root of 100000 by the long division method as follows: 100000 is 489 (4389 − 3900) less than 317 2.

Answer 2

Step-by-step explanation:

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)(576=242) and the nearest smaller perfect square is \left(625=25^{2}\right).(625=252).

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)(576=242) is not taken into consideration.

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