Root Calculator
Calculate nth root of a number.
Root Calculation
2 = square root, 3 = cube root, etc.
Expression:
√16
Root Result
Square Root
4.000000
Verification:
(4.0000)2 = 16.0000 ✓
Formula
√16 = 16^(1/2) = 4.0000
Common Roots:
Square root (most common)
About This Calculator
The Root Calculator helps you calculate the nth root of a number. The nth root of a number x is a number that, when raised to the power n, equals x. Common roots include square root (n=2) and cube root (n=3).
Enter the number and the root value (2 for square root, 3 for cube root, etc.), and the calculator will compute the root. The calculator supports positive numbers for any root, and negative numbers for odd roots (cube root, 5th root, etc.).
Formula & Calculation Method
Root Formulas:
Nth Root:
ⁿ√x = x^(1/n)
Common Roots:
Square Root (n=2): √x = x^(1/2)
Cube Root (n=3): ∛x = x^(1/3)
Fourth Root (n=4): ⁴√x = x^(1/4)
Properties:
(ⁿ√x)ⁿ = x
ⁿ√(x × y) = ⁿ√x × ⁿ√y
ⁿ√(x / y) = ⁿ√x / ⁿ√y
Roots are the inverse operation of exponents. The square root of x is the number that, when squared, equals x. For negative numbers, only odd roots (3rd, 5th, etc.) yield real results.
How to Use This Calculator
- Enter Value: Input the number you want to find the root of.
- Enter Root: Input the root value (2 for square root, 3 for cube root, etc.).
- View Results: See the calculated root and verification.
- Note: Even roots of negative numbers are not real numbers (they're complex).
Frequently Asked Questions
What is a square root?
The square root of a number x is a number that, when multiplied by itself, equals x. For example, the square root of 16 is 4 because 4 × 4 = 16. It's written as √x or x^(1/2).
Can I calculate roots of negative numbers?
Yes, but only for odd roots (3rd, 5th, 7th, etc.). Even roots (2nd, 4th, 6th, etc.) of negative numbers are not real numbers - they are complex numbers. For example, √(-4) is not a real number, but ∛(-8) = -2.
What is the difference between root and exponent?
Roots and exponents are inverse operations. If x^n = y, then the nth root of y is x. For example, if 2³ = 8, then the cube root of 8 is 2. Roots "undo" exponents.
How do I calculate higher roots?
Higher roots (4th, 5th, etc.) work the same way as square and cube roots. Use the formula ⁿ√x = x^(1/n). For example, the 5th root of 32 is 32^(1/5) = 2, because 2⁵ = 32.
Expert Reviewed
This calculator was reviewed by NumCalculators Editorial Team, Multi-disciplinary Expert Team