State true/false:
The square root of 196 by the method of repeated subtraction is 14.

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Detailed Solution

The square root of 196 can be obtained by the method of repeated subtraction as follows:

(i) 196-1=195 (ii) 195-3=192 (iii) 192-5=187

(iv) 187-7=180 (v) 180-9=171 (vi) 171-11=160

(vii) 160-13=147 (viii) 147-15=132 (ix) 132-17=115

(x) 115-19=96 (xi) 96-21=75 (xii) 75-23=52

(xiii) 52-25=27 (xiv) 27-27=0.

We subtracted successive odd numbers starting from 1 to 196 and obtained 0 at the 14^th step.

Therefore, $\sqrt{196} = 14$ .

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