Question

Find the square root of 144 by the method of repeated subtraction.
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Answer 1

Answer:

72 is the square route of 144

Answer 2

                                                                                                                                                 

As explained in Properties of Square Numbers the square number is the sum of successive odd numbers starting from 1 and you can find the square root of a number by repeatedly subtracting successive odd numbers( which is also starting from 1) from the given square number, till you get zero.  

1. $144-1=143$

2.  $143-3=140$

3.$140-5=135$

4. $135-7=128$

5. $128-9=119$

6. $119-11=108$

7. $108-13=95$

8. $95-15=80$

9. $80-17=63$

10. $63-19=44$

11. $44-21=23$

12. $23-23=0$

∴  $\sqrt{144}=12$

                                                                                                                                                 

may be it is helpful for you