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Question:

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

Solution:

(i)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 get 0 in the 10th step. So, √100=10
(ii)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 get 0 in 13th step. So, √169=13.