How to use it
- Set the coefficient and choose the root index.
- Type the number under the root and choose whether the root sits in the numerator or the denominator.
- Add another denominator if the expression has one.
How it works
The radicand is factored by trial division into primes pⁱ. For an n-th root the integer part of i ÷ n is moved outside the root and the remainder stays inside. Everything is done in exact integers; the decimal value is only for checking. For a root in the denominator, the numerator and denominator are multiplied by ⁿ√(rⁿ⁻¹), where r is the radicand left after simplifying, and the result is simplified again.
Worked example
6 ÷ √12: first √12 = 2√3, so the expression is 6 ÷ (2√3) = 3 ÷ √3. Multiplying by √3/√3 gives 3√3 ÷ 3 = √3. Enter coefficient 6, radicand 12, root in the denominator and the tool returns √3.
Tips
- Check the decimal value against a calculator to catch a typo.
- Only the radicand is under the root: for √(2/3) enter it as √2 ÷ √3 by hand first, using the denominator mode.