Root calculator
Find a square root, cube root or any nth root, and see the exact simplified radical when the answer is not a whole number. It is useful for algebra homework and checking geometry answers.
- Runs in your browser
- Free, no account needed
- Copy or download the result
Result
Example
Number: 72 Root: Square root N for nth root (2 to 100): 4
Square root of 72 Simplified radical form: 6√2 (6 sqrt(2)) Decimal: 8.48528137424 Decimal rounded to 12 significant digits.
How to use the root calculator
- Type the Number, such as 72.
- Choose a Root: Square root, Cube root or Nth root. For an nth root, set N for nth root (2 to 100).
- Press Run to see the exact or simplified answer and the decimal.
- Press Copy result or Download to keep the answer.
How it works
For whole numbers, the tool first checks for a perfect power, so √144 = 12 and the cube root of -27 = -3. It can check whole numbers up to 300 digits.
For whole numbers up to 10^12 that are not perfect powers, it pulls out every factor it can, such as √72 = 6√2 and the cube root of 54 = 3∛2.
Even roots of negative numbers are rejected because they are not real. Odd roots of negative numbers are negative.
Decimal answers use floating point and are rounded to 12 significant digits.
Everything runs in your browser. Your input is not uploaded or stored.
Questions and answers
How do you simplify a square root?
Find the largest perfect square that divides the number and take its root outside. 72 = 36 x 2, so √72 = 6√2.
Can you take the cube root of a negative number?
Yes. The cube root of -27 is -3, because (-3)^3 = -27. Even roots of negative numbers are not real numbers.
What is an nth root?
The nth root of x is the number that gives x when raised to the power n. The 4th root of 16 is 2.