How to Use This Root Calculator
Enter the number you want to find the root of (called the radicand) and the root degree. For square root, leave the degree as 2. Click "Calculate Root" and the result will appear instantly. You can compute cube roots (degree = 3), 4th roots, or any nth root – even decimal degrees like 1.5.
What is a Root in Mathematics?
In mathematics, the nth root of a number x is a value r such that rⁿ = x. The most common roots are the square root (n=2) and the cube root (n=3). The symbol √ is called a radical, and the expression n√x represents the nth root of x.
Types of Roots
Square Root
Square root (√x) answers the question: "What number multiplied by itself gives x?" For example, √25 = 5 because 5 × 5 = 25. Every positive number has two square roots: a positive and a negative (e.g., ±5). This calculator returns the principal (non‑negative) root for even degrees.
Cube Root
Cube root (∛x) finds a number that when cubed equals x. Example: ∛-8 = -2 because (-2)³ = -8. Unlike square roots, cube roots of negative numbers are real.
Higher Roots
For any degree n (4th root, 5th root, etc.), the same principle applies. Odd-degree roots preserve the sign of the radicand; even-degree roots of negative numbers are not real (the calculator will show "not a real number").
Properties of Radicals
• √(a × b) = √a × √b (product property)
• √(a / b) = √a / √b (quotient property)
• (ⁿ√a)ⁿ = a
• ⁿ√(aⁿ) = |a| when n is even, and = a when n is odd.
Frequently Asked Questions
Q: What is the difference between a square root and an nth root?
A: A square root is simply the case where n = 2. The nth root generalises the concept: ⁿ√x is the number that, when raised to the power n, gives x.
Q: Can this calculator find the root of a negative number?
A: Yes, but only for odd root degrees (like 3, 5, 7…). For even degrees, the result is not a real number, and the calculator will show an error message.
Q: How do I calculate the 4th root of 16?
A: Enter 16 as the number, set the root degree to 4, and click Calculate. The result will be 2, because 2⁴ = 16.
Q: Is this root calculator free to use?
A: Absolutely! It’s a completely free online tool built directly into this page. No downloads or sign‑ups required.
