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Find the square roots of 100 by 169 the method of repeated subtraction.

Q.3  Find the square roots of 100 and 169 by the method of repeated subtraction.

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(i)   For 100 :-  100 - 1 = 99

      99 - 3 = 96

      96 - 5 = 91

      91 - 7 = 84

      84 - 9 = 75

      75 - 11 = 64

      64 - 13 = 51   

      51 - 15 = 36                

      36 - 17 = 19

      19 - 19 = 0.

We obtain zero at 10th step so \sqrt{100} = 10

 

(ii)    For 169 :- 169 - 1 = 168

        168 - 3 = 165

        165 - 5 = 160

        160 - 7 = 153

        153 - 9 = 144

        144 - 11 = 133

        133 - 13 = 120   

        120 - 15 = 105

        105 - 17 =  88

         88 - 19 = 69 

         69 - 21 = 48

         48 - 23 = 25;

         25 - 25 = 0.

  We obtain Zero at the 13th step so \sqrt{169} = 13

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