Question

Find the least number that should be added to 9108 to make it a perfect square. Also find the square root of the number obtained.
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Answer 1

Question :- Find the least number that should be added to 9108 to make it a perfect square. Also find the square root of the number obtained.

Solution :-

finding the square root of 9108 by long division method first we get,

) 91 - 08 (

• upto 91 we can go to square of 9 => 9² = 81

so,

9 ) 91 - 08 (9

-81

10-08

now, taking next pair down and adding same quotient ,

18x ) 1008 (

as we can see

• highest value of x can be = 185 × 5 = 925

then,

185) 1008 (5

- 925

83

therefore, we can conclude that,

• 9108 is near to the square of 95 .

so,

→ 95² < 9108 < 96²

→ 9025 < 9108 < 9216

hence,

→ Required Number = 9216 - 9108 = 108 (Ans.)

∴ 108 is the least number that should be added to 9108 to make it a perfect square.

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Answer 2

Given : Number 9108

To Find : least number that should be added to 9108 to make it a perfect square

Solution:

                 95

                 9108

          9     81

                _____

                  1008

      185        925

                 ______

                       83

  =>  96  > √9108  > 95

Hence next perfect square is 96²

(96)²

= (100 - 4)²

= 100² + 4²  - 2(100)4

= 10000 + 16 - 800

= 9216

9216 - 9108 =  108

Hence 108 must be added to 9108 to make it perfect square

and square root of the number so obtained is 96.

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