question_answer 1)

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

Answer:

                (i) 100 (i) \[100-1=99\] (ii) \[99-3=96\] (iii) \[~96-5=91\] (iv) \[91-7=84\] (v) \[84-9=75\] (vi) \[75-11=64\] (vii) \[64-13=51\] (viii) \[51-15=36\] (ix) \[36-17=19\] (x) \[~19-19=0\] Since from 100 we subtracted successive odd numbers starting from 1 and obtained 0 at the 10th step. Therefore, \[\sqrt{100}=10\]. (ii) 169 (i) \[169-1=168\] (ii) \[168-3=165\] (iii) \[165-5=160\] (iv) \[160-7=153\] (v) \[153-9=144\] (vi) \[144-1=133\] (vii)  \[133-13=120\] (viii) \[120-15=105\] (ix) \[105-17=88\] (x) \[88-19=69\] (xi) \[69-21=48\] (xii) \[48-23=25\] (xiii) \[25-25=0\] Since from 169 we subtracted successive odd numbers starting from 1 and obtained 0 at the 13th step, therefore, \[\sqrt{169}=13\].