Find the square roots of following numbers by the method of repeated subtraction
1.121
2.144
3.64
4.81
5.36
Answers
Answer:
We need to find square root of 121 by repeated subtraction method.
121−1=120
120−3=117
117−5=112
112−7=105
105−9=96
96−11=85
85−13=72
72−15=57
57−17=40
40−19=21
21−21=0
We have subtract odd numbers from the given number.
So, we start with subtracting 1 form 121 which gives us 120.
Now, subtract 3 from 120 which is 117.
The process continues till we get the final answer as 0.
The number of steps for which this operation has been performed will give the square root of the number.
In this case, we had to subtract in 11 steps to get to 0. Hence, root of 121 is 11.
2) 144 - 1 = 143
143 - 3 = 140
140 - 5 = 135
135 - 7 = 128
128 - 9 = 119
119 - 11 = 108
108 - 13 = 95
95 - 15 = 80
80 - 17 = 63
63 - 19 = 44
44 - 21 = 23
23 - 23 = 0
Since the last difference is zero, 144 is a perfect square.
The square root of 144 is 12 as we have performed repeated subtraction 12 times and after the 12 the subtraction, the remainder is zero.
3) The value of square root 64 by repeated subtraction method is 8. This can be done as, 64 – 1 = 63, 63 – 3 = 60, 60 – 5 = 55, 55 – 7 = 48, 48 – 9 = 39, 39 – 11 = 28, 28 – 13 = 15, 15 – 15 = 0.
4) The steps to find the square root of 81 is: 81 – 1 = 80. 80 – 3 = 77. 77 – 5 = 72.
5) i. 36-1= 35
ii. 35-3= 32
iii. 32-5= 27
iv. 27-7-20
v. 20-9= 11
vi. 11-11-0
so the square root of 36 is 6.