Root Calculator - Square Root, Cube Root & Nth Root Calculator
Free online root calculator for square roots, cube roots, and nth roots. Calculate roots with precision and step-by-step verification.
Enter Values
Root Result
Enter a number and root to calculate
About Root Calculator
The Root Calculator calculates the nth root of a number using the formula: ⁿ√x = x^(1/n)
Types of 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)
- Nth Root (n=any): ⁿ√x = x^(1/n)
Properties:
- √(a × b) = √a × √b
- √(a ÷ b) = √a ÷ √b
- (ⁿ√x)ⁿ = x
- ⁿ√(xⁿ) = |x| (for even n)
Applications:
- Solving quadratic equations
- Calculating distances and magnitudes
- Engineering and physics calculations
- Financial mathematics (compound interest)
Note: For even roots, the result is always positive. For odd roots, the result can be negative if the input is negative.
Frequently Asked Questions
What is a square root?
A square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 9 is 3 because 3 × 3 = 9.
What is a cube root?
A cube root of a number is a value that, when multiplied by itself three times, gives the original number. For example, the cube root of 8 is 2 because 2 × 2 × 2 = 8.
How do I calculate nth roots?
The nth root of a number x is calculated as x^(1/n). For example, the 4th root of 16 is 16^(1/4) = 2, because 2^4 = 16.
Can I calculate roots of negative numbers?
For even roots (square root, 4th root, etc.), negative numbers don't have real roots. For odd roots (cube root, 5th root, etc.), negative numbers have real roots.
What's the difference between square root and cube root?
Square root finds what number multiplied by itself equals the original number. Cube root finds what number multiplied by itself three times equals the original number.