Steps | 963 | ||
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 twice the deficiency from that number | In this case, 96 - (2 × 4) = 88 |
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4. | Set-up twice of as many Zeroes, as the Base | In this case, 100 has two Zeroes. So, we get 88,0000 |
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5. | Multiply thrice the Deficiency, with the Deficiency - and set-up as many Zeroes as the Base. | In this case, (3 × 4) × 4 = 12 × 4 = 48 And set-up with two Zeroes, we get 4800 |
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6. | Cube the Deficiency, and subtract from the sum previous numbers to get the answer. | In this case, 43 = 64 And, 88,00,00 + 48,00 - 64 = 884736, which is the answer! |
The Base is 100 and, the Deficiency is: 100 - 103 = -3 = 3 And, 33 = 27 Also, (3 × 3) × 3 = 27 Now, 103 - (2 × 3) = 103 + 6 = 109 Also, 109,00,00 + 2700 = 1092700 And, 1092700 - 27 = 1092700 + 27 = 1092727, which is the answer! |
Clearly, the Deficiency is 9 And, 93 = 729 Also, (3 × 9) × 9 = 243 Now, 991 - (2 × 9) = 991 - 18 = 973 Also, 973,000,000 + 243,000 = 973,243,000 And, 973,243,000 - 729 = 973242271 Thus, 9913 = 973,242,271 |
Clearly, the Deficiency is 6 And, 63 = 216 Also, (3 × 6) × 6 = 108 Now, 10006 - (2 × 6) = 10006 + 12 = 10018 Also, 10018,0000,0000 + 108,0000 = 10018,0108,0000 And, 10018,0108,0000 - 216 = 10018,0108,0000 + 216 = 10018,0108,0216 Thus, 100063 = 1,001,801,080,216 |
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, N3 = (a - b)3 = a3 - 3a2b + 3ab2 - b3 = a3 - a2b - 2a2b + 3ab2 - b3 = a2(a - b - 2b) + a(3b × b) + b3 But, N = a - b. So, substituting a = N + b N3 = a2(N + b - b - 2b) + a(3b × b) + b3 = a2(N - 2b) + a(3b × b) + b3 This is exactly what this Upasūtra makes us do. |
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