Finding the Square root through Subtraction of successive odd numbers
Finding square root through repeated subtraction
Do you remember that the sum of the first n odd natural numbers is
Consider
81 – 1 =
80 – 3 =
77 – 5 =
Continue this pattern
81 -1, 80 -3,
Pattern: “Successively subtract 1, 3, 5, 7, 9, ... from it, to get the next one.”
From 81 we have subtracted successive odd numbers starting from 1 and obtained 0 at 9th step. Therefore
Can you find the square root of 729 using this method? It is possible but it will be time consuming. Thus, we need a simpler way to find the square roots.
TRY THESE
By repeated subtraction of odd numbers starting from 1, find whether the following numbers are perfect squares or not? If the number is a perfect square then find its square root.
(i)
(i) 121
81 – 1 =
80 – 3 =
77 – 5 =
72 – 7 =
65 – 9 =
56 – 11 =
45 – 13 =
32 – 15 =
17 – 17 =
Yes, it is a perfect square.
(ii)
(ii) 55
55 – 1 =
54 – 3 =
51 – 5 =
46 – 7 =
39 – 9 =
30 – 11 =
19 – 13 =
6 – 15 =
No, it isn't a perfect square.
(iii)
(iii) 36
36 – 1 =
35 – 3 =
32 – 5 =
27 – 7 =
20 – 9 =
11 – 11 =
Yes, it is a perfect square.
(iv)
(iv) 49
49 – 1 =
48 – 3 =
45 – 5 =
40 – 7 =
33 – 9 =
24 – 11 =
13 – 13 =
Yes, it is a perfect square.
(v)
(v) 90
90 – 1 =
89 – 3 =
86 – 5 =
81 – 7 =
74 – 9 =
65 – 11 =
54 – 13 =
41 – 15 =
26 – 17 =
9 – 15 =
No, it isn't a perfect square.