About this tool
Turn an unwieldy root into its simplest radical form. Enter an integer radicand and an index (2 for a square root, or any nth root) and the tool returns the simplified form such as 6√2, along with the coefficient pulled outside the radical, the number left inside, and the decimal value. It works entirely in your browser and updates as you type.
The method is prime factorization. The radicand is broken into prime powers, and for an index n each prime contributes p^floor(e/n) to the outside coefficient and p^(e mod n) to the part left inside. For a square root that means extracting pairs, so √72 = √(2^3 * 3^2) = 6√2. A perfect nth power simplifies to a plain integer, and if nothing can be pulled out the radical is already in simplest form.
Negative radicands are allowed for odd roots (the sign comes outside), but an even root of a negative number is not a real number and is flagged rather than shown. Use it to tidy answers, rationalize working, or check a simplification by hand.