Mathematics in Ancient and Medieval India c5.s9.14

c5.s9.14

| | *Āryabhaṭa I's method* | *Modern method* |
| Subtract the cube 1³ = 1 | 1 9 5 3 1 2 5 (cube root 1 1 ..... | 1953125 | 125 1 |
| | 9 | 953 |
| Divide by thrice the square of the root i e. 3 × 1² | 3) 6 (2....... (a) 3 5 | 1² × 300 & / = 300 & / 1 × 30·2 & / = 60 & / 2² = 4 & / 364 & |
| Subt. the square of the quotient multiplied by thrice the previous root i.e , 2² × 3 × 1 = 12 | 1 2 .......(b) | 728 |
| | 2 3 3 | 225125 |
| Subt. the cube of the quotient i.e., 2³ = 8 | 8....... (c) | 12² × 300 & / = 43200 & / 12 × 30 × 5 & / = 1800 & / 5² = 25 & / 45025 & |
| | 2 2 5 1 | 225125 |
| Divide by thrice the square of the quotient i.e., 3 × 12² = 432 | 432) 2 1 6 0 (5...(a') | |
| Subt. sq. of the quotient multiplied by thrice the previous root i.e., 5² × 3 × 12 = 900 | 9 1 2 9 0 0 ....(b') | |
| | 1 2 5 | |
| Subt. cube of the quotient i.e , 5³ = 125 | 1 2 5....(c') | |
| | ∴ cube root of 1953125 = 125. | |