Question

The smallest number that should be added to or subtracted from the sum of squares of 9 and 10 to make it a perfect square is​

Answer 1

Given:

Two number: 9 and 10

To find:

The smallest number that should be added to or subtracted from the sum of squares of 9 and 10 to make it a perfect square.

Solution:

The sum of squares of 9 and 10 are:

9² + 10² = 81 + 100 = 181

The next perfect square is 196 and the previous perfect square is 169.

So the closes perfect square to the number 181 is 169 and the difference between them is 12.

Therefore the smallest number that should be subtracted from the sum of squares of 9 and 10 to make it a perfect square is 12.

Answer 2

Given :  number that should be added to or subtracted from the sum of squares of 9 and 10 to make it a perfect square

To Find : Smallest Number

Solution:

9² = 81

10² = 100

9² + 10²  = 81 + 100 = 181

        13

       181

1       1

     ________

        81

23    69

       ____

          12

√(181 - 12)  = 13

Hence 12 should be subtracted to get perfect square of 13

Next perfect square will be 14²  = 196

196 - 181 = 15

15 Should be added to get perfect square of 14

in 12 and 15

12 < 15

Hence 12 is the smallest number that should be  subtracted from the sum of squares of 9 and 10 to make it a perfect square

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