Steps | 962 | ||
1. | Consider the nearest power of 10 as the Base | In this case, the Base, closest to 96, is 100. | |
2. | Find the deficiency, and represent as Rekhank for negative deficiency. | In this case, the Deficiency = 100 - 96 = 4 |
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3. | Subtract the deficiency from that number | In this case, 96 - 4 = 92 |
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4. | Set-up as many Zeroes, as the Base | In this case, 100 has two Zeroes. So, we get 9200 |
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5. | Square the Deficiency, and add to get the answer | In this case, 42 = 16 And, 9200 + 16 = 9216, which is the answer! |
The Base is 100 and, the Deficiency is: 100 - 103 = -3 = 3 And, 32 = 9 Also, 103 - 3 = 103 + 3 = 106 And, 10600 + 9 = 10609, which is the answer! |
Clearly, the Deficiency is 9 And, 92 = 81 Also, 991 - 9 = 982 And, 982,000 + 81 = 982,081 Thus, 9912 = 982,081 |
Clearly, the Deficiency is 6 And, 62 = 36 Also, 10006 - 6 = 10006 + 6 = 10012 And, 10012,0000 + 36 = 10012,0036 Thus, 100062 = 100,120,036 |
Assuming N is a number close (and less) to a power of 10, then N = a - b 'a' being the power of 10, and 'b' being the Deficiency Now, N2 = (a - b)2 = a2 - 2ab + b2 = a (a - 2b) + b2 But, N = a - b. So, substituting a = N + b N2 = a ([N + b] - 2b) + b2 = a (N - b) + b2 This is exactly what this Upasūtra makes us do. |
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