About the root calculator
The root calculator finds square roots, cube roots and any nth root of a number. For square roots of whole numbers it also shows the simplified radical form, and it flags perfect squares and perfect powers.
Negative numbers are handled where a real answer exists: odd roots of negatives are real, and square roots of negatives are shown as imaginary numbers.
Who should use the root calculator
- Students simplifying radicals or checking roots.
- Builders and designers working with areas and volumes.
- Anyone who needs an nth root without a scientific calculator.
How to use the root calculator: what each input means
- Root degree (n)
- A whole number from 1 up: 2 for a square root, 3 for a cube root, and so on.
- Number
- The radicand, the number under the root sign.
How the root calculator works: method and formula
The nth root of x is x raised to the power 1 ÷ n. For square roots of whole numbers, the calculator divides out the largest square factor to give the simplest radical form, so √72 becomes 6√2 because 72 = 36 × 2.
- nth root
- ⁿ√x = x^(1/n)
- Simplifying
- √(a² × b) = a√b
How to read your root calculator result
The check line raises the answer back to the power n so you can see it reproduces the original number. Only the principal real root is shown; an even root of a positive number also has a negative root of the same size.
Root Calculator worked example
Find the square root of 72.
- 72 = 36 × 2 and 36 = 6², so √72 = 6√2.
- Numerically, 6 × √2 = 8.485281374.
- Check: 8.485281374² = 72.000000.
√72 = 6√2 ≈ 8.485281374.
Practical uses of the root calculator
- Simplifying radicals in algebra.
- Finding the side of a square from its area.
- Calculating cube roots for volumes.
Assumptions and limitations of this calculator
- Radical simplification applies to square roots of positive whole numbers within safe integer size.
- Even roots of negative numbers other than square roots are reported as not real; complex roots are not displayed.