The document describes three methods for finding square roots: repeated subtraction, prime factorization, and long division. It provides examples of using the repeated subtraction method to find the square root of 64 and 169 by successively subtracting odd numbers from the original number until reaching zero, with the number of subtractions equaling the square root. It also lists several numbers and asks to find their square roots using this method.

1. Mostly we used the following methods to
find square roots.
1-Repeated subtraction method
2-Prime factorization method
3- Long division method

2. Step1:-
Successively subtract 1,3,5,7…….
From the given number till we get
zero.
Step 2:-
Cont the number of times the
subtraction is performed to arrive
at zero. This number gives the
square root of the given number.
Here successive subtraction is performed 8 times to arrive at
zero. So the square root of 64 is 8.

3.  Let’s performed successive subtraction to find the
square root of 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
So we had to performed 13
times successive
Subtraction to arrive at
zero.
Hence square root of 169 is
13.

4. 125
81
100
196
256