Radicals are roots: square roots, cube roots and higher. In exact maths they are kept in simplified radical form rather than rounded, which makes later steps cleaner and answers exact.
How to use the Radical Calculator
- Number (radicand)
- Radical degree n
Everything is calculated in your browser, so results appear instantly and nothing you type is sent to a server.
How it works
The decimal value uses x^(1/n). For whole numbers the calculator factorises x and moves every group of n identical prime factors outside the radical.
Formula
ⁿ√x = x¹/n), ⁿ√(aⁿ·b) = a·ⁿ√b
Worked example
Inputs — Number (radicand): 72; Radical degree n: 2.
Results — Simplified radical = 6√2; Decimal value = 8.48528137424.
Key terms
- Radical
- An expression with a root sign.
- Index
- The degree n of the root.
Frequently asked questions
What is the radicand?
The number under the radical sign.
How do I simplify √50?
50 = 25 × 2, so √50 = 5√2.
What is the index of a radical?
The degree n in ⁿ√x; square roots have index 2.
Can I take an even root of a negative number?
Not in the real numbers.