Root Calculator
Enter a number and the root you want (2 for square, 3 for cube, or any n). The calculator gives the exact decimal value and simplified radical form.
N-th Root & Radical Simplifier
Root & Radical Result
What is a root?
The nth root of a number x is the value that, multiplied by itself n times, gives x. For example the 4th root of 16 is 2 because 2 × 2 × 2 × 2 = 16. The square root (n = 2) and cube root (n = 3) are the most common.
Roots and exponents are inverse operations: the nth root of x equals x^(1/n). A fractional exponent like 1/2 is another way of writing a square root.
Simplified radical form
Many roots are not whole numbers, but they can still be written exactly. For example √72 = 6√2 because 72 = 36 × 2 and √36 = 6. This 'simplified radical form' keeps answers exact instead of rounding.
The calculator extracts the largest perfect power from under the radical. It also handles odd roots of negative numbers, which are defined for real numbers (for example ∛(-8) = -2).
How to use this calculator
- Enter the number you want to take a root of.
- Enter the root value (2 for square, 3 for cube, any n for nth root).
- Press Calculate to see the decimal value.
- Read the simplified radical form when one exists.
Pro tips
- Use root 2 for square roots and root 3 for cube roots.
- To take a fourth root of 16, enter 16 with root 4.
- Odd roots (3, 5, 7...) work with negative numbers; even roots do not.
Advantages & considerations
✅ Advantages
- Any root from square to nth
- Simplified radical form for exact answers
- Shows a verification check for every result
⚠️ Considerations
- Even roots of negative numbers are not real
- Non-integer roots are evaluated numerically