Calculate square roots, cube roots, or any nth root instantly. Results update as you type.
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The square root of a number is a value that, when multiplied by itself, gives the original number. √25 = 5 because 5 × 5 = 25.
The cube root of a number is a value that, when multiplied by itself three times, gives the original. ³√27 = 3 because 3 × 3 × 3 = 27.
Enter any root degree in the 'n' field. A 4th root of 81 is 3 (because 3⁴ = 81). A 2nd root is the same as a square root.
Square roots of negative numbers are undefined in real numbers (they produce imaginary results). Odd roots like cube roots do work with negatives: ³√−8 = −2.
Most roots are irrational numbers with infinite decimals. Use the decimal places setting to control how many digits you see in the result.
The nth root of x equals x raised to the power 1/n. This means ⁴√16 = 16^(0.25) = 2. Your scientific calculator can compute this the same way.
Calculate the square root, cube root, or any nth root of any number instantly. Enter the number and root degree and the result appears immediately.
Square root of 144 (n = 2)
Result: 12
Cube root of 27 (n = 3)
Result: 3
4th root of 256 (n = 4)
Result: 4
5th root of 100,000 (n = 5)
Result: 10
Square root of 225
Result: 15
Cube root of 125
Result: 5
The radical symbol (√) was first used by Christoph Rudolff in his 1525 algebra textbook. It is widely believed to derive from a stylised lowercase 'r', the first letter of the Latin 'radix' meaning 'root'. The vinculum — the horizontal bar extending over the number — was added later by René Descartes in 1637.
The nth root of a number is a value that produces the original number when raised to the power n. A square root uses n = 2 and a cube root uses n = 3. For example, the cube root of 27 is 3 because 3 × 3 × 3 equals 27.
Within the real numbers, an even power cannot produce a negative result, so a negative number has no real square root, fourth root, or other even root. Complex-number systems can represent those answers, but this calculator reports ordinary real-number results and should not be used as a complex algebra solver.
Many roots are irrational numbers whose decimal digits continue without repeating. The decimal-place control rounds the displayed value so it is easier to read and copy. Keep more digits during intermediate calculations and round only the final answer when precision matters.
Raise the displayed root to the selected degree and compare it with the original number. A rounded root may produce a nearby value rather than an exact match, so use additional decimal places for the check. For coursework or engineering work, retain the exact radical form when the method requires it.