Find the square root, cube root or any nth root of a number, including odd roots of negative numbers.
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With number (x) 729, root degree (n) 3, the root is 9.
| Number (x) | 729 |
|---|---|
| Root degree (n) | 3 |
| Root | 9 |
|---|---|
| Square root | 27 |
| Cube root | 9 |
Enter the number and the degree of the root: 2 for a square root, 3 for a cube root and so on. The nth root is the number that gives x when raised to the power n. Even roots of negative numbers are not real numbers, while odd roots of negative numbers are simply negative. The square root and cube root are shown alongside for comparison.
ⁿ√x = x^(1/n). An odd root of a negative number is negative: ³√(−27) = −3. Enter the number and the degree of the root: 2 for a square root, 3 for a cube root and so on. The nth root is the number that gives x when raised to the power n. Even roots of negative numbers are not real numbers, while odd roots of negative numbers are simply negative. The square root and cube root are shown alongside for comparison.
With number (x) 729, root degree (n) 3, the root is 9. Square root: 27; Cube root: 9.
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9, because 9 × 9 × 9 = 729.
Both 3 and −3 square to 9, but the √ symbol means the principal root, which is the non-negative one. Equations like x² = 9 have both answers: x = 3 or x = −3.
Find the perfect squares on either side. √50 lies between √49 = 7 and √64 = 8, close to 7. Refine with the average of 7 and 50 ÷ 7: (7 + 7.14) ÷ 2 ≈ 7.07, which is accurate to two decimals.