The Root Calculator finds the square root, cube root or any nth root of a number.
| √16 | 4 |
| ∛27 | 3 |
| 4√16 | 2 |
The nth root of x is the number that, multiplied by itself n times, gives x. The square root of 16 is 4 because 4 × 4 = 16; the cube root of 27 is 3 because 3 × 3 × 3 = 27. Roots are the inverse of powers: ⁿ√x = x^(1/n).
Every positive number has two square roots, one positive and one negative; the √ symbol means the positive (principal) one. Perfect squares such as 1, 4, 9, 16, 25 have whole-number roots; others, such as √2 ≈ 1.41421356, are irrational.
Find the nearest perfect powers and refine. √50 lies between 7 (49) and 8 (64), close to 7.07. Newton's method improves a guess g with g ← (g + x/g)/2 and converges very fast.
Odd roots of negative numbers are real (∛−8 = −2). Even roots of negative numbers are not real; they are imaginary, e.g. √−4 = 2i.
What is √0? 0.
Is √(a × b) = √a × √b? Yes, for non-negative a and b.
What is a radical? Another name for a root expression.