Root Calculator
Square roots, cube roots and any nth root, simplified exactly (√27 = 3√3) with the decimal value.
Change the values and press Calculate to work out your own figures.
Square root
Enter a number.
Show the working
- √27 = 3√3 = 5.19615242271
Cube root
Enter a number (negatives allowed).
Show the working
- ∛-54 = -3∛2 = -3.77976314968
Any root
Enter the root n and the number.
Show the working
- ⁸√15 = ⁸√15 = 1.40285055201
How to use it
Enter a number. Enter a number (negatives allowed). Enter the root n and the number.
Number boxes accept whole numbers, decimals, fractions (3/4), powers (2^10), roots (sqrt(2)) and the constants pi and e. Show the working lists the steps.
Key facts
ⁿ√x = x^(1/n)
Simplifying
Pull out perfect powers: √27 = √(9 × 3) = 3√3.
Questions
What is √27?
3√3 ≈ 5.19615242271.
Can I take a cube root of a negative number?
Yes: ∛−54 = −3∛2.
Formulas
ⁿ√x = x^(1/n)
Sources
Limitations
- Expressions up to 500 characters; matrices up to 10 × 10.
- Big-number results up to 100,000 digits; factorials up to 10,000!.
- Numbers in words up to 10^102 (short scale).