Calculate any nth root instantly. Find the root value by entering a number and the root degree (square root, cube root, or beyond).
nth Root Result
3
Number (x)27
Root Degree (n)3
Square Root5.196152422706632
Cube Root3
x^(1/n)3
Verification (result^n)27
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What is the Root Calculator?
A root is the inverse operation of exponentiation. The nth root of x is the number that, when raised to the power n, equals x. For example, the cube root of 27 is 3 because 3³ = 27. This calculator finds any nth root for positive or negative numbers (handling odd roots of negatives correctly).
How it works
Enter the number (x) you want to find the root of and the root degree (n). The calculator uses the formula x^(1/n) to compute the result. It also displays the square root, cube root, and a verification (result^n should equal x) to confirm accuracy.
nth Root of x = x^(1/n)
The nth root is computed by raising the number to the power of 1/n. For example, the square root of 16 is 16^(1/2) = 4. The cube root of 8 is 8^(1/3) = 2. Negative numbers can have real odd roots (like the cube root of −8 = −2), but even roots of negative numbers are not real.
Examples
Input
Result
Notes
x = 27, n = 3
3
The cube root of 27 is 3, since 3 × 3 × 3 = 27
x = 16, n = 2
4
The square root of 16 is 4, since 4 × 4 = 16
x = 32, n = 5
2
The fifth root of 32 is 2, since 2^5 = 32
How to use the Root Calculator
Enter the number (x) from which you want to find the root
Enter the root degree (n)—use 2 for square root, 3 for cube root, etc.
The calculator instantly computes x^(1/n) and displays the result
Review the square root, cube root, and verification stats to understand the calculation
Check the verification (result^n) to confirm it equals (or is very close to) your original number
For negative x with odd n, the result is the negative of the positive root
Benefits
Instantly find any nth root without manual calculation or trial-and-error
Handles both positive and negative numbers correctly (including odd roots of negatives)
Displays square root and cube root automatically for quick reference
Verification stat confirms accuracy by showing result^n
Perfect for algebra, geometry, science, and engineering calculations
Free, fast, and no sign-up required
Tips & common mistakes
Common mistakes
Confusing the root degree n with the exponent—remember, the nth root is x^(1/n), not x^n
Trying to take an even root of a negative number (e.g., square root of −4 is not real)
Not recognizing that negative numbers can have real odd roots (e.g., cube root of −8 = −2)
Ignoring floating-point rounding—result^n might be very close to x but not exactly equal
Tips
Fractional roots and exponents are inverses: square root of x = x^0.5, cube root = x^(1/3)
Use verification to check your answer—if result^n equals x, your root is correct
For very large or very small numbers, the result may display in scientific notation
The 4th root of 16 is 2 (since 2^4 = 16), the 5th root of 32 is 2 (since 2^5 = 32)
Frequently asked questions
What is the difference between a root and an exponent?
An exponent means multiply; an root means divide the exponent. The square root of 16 is 16^(1/2) = 4, the inverse of 4² = 16.
Can I take the square root of a negative number?
No, the square root of a negative number is not a real number. Even roots (2nd, 4th, 6th) of negative numbers are undefined in real mathematics. However, odd roots (3rd, 5th) of negative numbers are real and negative.
What is the cube root of −8?
The cube root of −8 is −2, because (−2)³ = −8. Odd roots of negative numbers always produce real negative results.
How do I verify my root is correct?
Raise the result to the power n. If result^n equals (or is very close to) your original number, your root is correct. This calculator shows the verification automatically.
What does the nth root mean?
The nth root of x is a number that, when raised to the power n, equals x. For example, the 4th root of 81 is 3, because 3⁴ = 81.
Can this calculator handle decimal root degrees?
Yes. For example, x^(1/2.5) is a valid calculation. Use decimal root degrees for fractional roots beyond simple square, cube, or higher integer roots.