Question

1)Find the least number that must be added to 9598 to make it a perfect square.2)Find the least number which must be subtracted from 2361 to make it aperfect square.3) Find the square root of 683.95 to 2 places of decimal.

Answer 1

the least number that should be added to 9598 is 6.9604 is the square root of 98.
57 is the least number that should be subtracted from 2361
the square root of 683.25 is 26.1524

Answer 2

Solution :-

Answer 1.

Least number that must be added to 9598 to make it a perfect square.

                97.96
           ____________
     9    |   9598.0000
     9    |   81
           |______
    187 |   1498
        7 |   1309 
           |_______
 1949  |    18900 
       9  |    17541
           |__________
19586 |      135900   
        6 |      117516
           |__________
           |        18384


Therefore, √9598 = 97.96

And, the nearest perfect square is 98².

⇒ 98² = 9604

⇒ 9604 - 9598 = 6

So, 6 is the least number which must be added to 9598 to make it a perfect square.

⇒ 9598 + 6 = 9604

And, √9604 = 98

_____________________________________________________________

Answer 2.

Least number which must be subtracted from 2361 to make it a perfect square.

              48
           __________
     4   |  2361
     4   |  16 
          |______
   88   |    761
     8   |    704        
          |_______
   96   |      57 
          |

So, on finding the square root of 2361, we get the quotient as 48 and the remainder as 57.

Hence, we will subtract 57 from 2361 to get the number which is a perfect square. 

⇒ 2361 - 57 = 2304

⇒ √2304 = 48

Therefore, 57 is the least number which must be subtracted from 2361 to make it a perfect square.

_____________________________________________________________

Answer 3

For the answer of the 3rd question, please have a look at the attachment.

Square root of 683.95 up to 2 decimal places.

⇒ √683.95 = 26.15

Thank you very much.