How this calculator works
Radicals with the same index combine under one root by multiplying or dividing their radicands. Even roots use the non-negative principal root and require non-negative radicands. Odd roots retain the sign of their radicand. The output shows a combined radical and decimal value; it does not factor out every perfect-power factor.
Formula
root_n(a) / root_n(b) = root_n(a/b), with b != 0.
Worked example
sqrt(50)/sqrt(2) = sqrt(25) = 5. cube_root(-54)/cube_root(2) = cube_root(-27) = -3.
Advertisement
Frequently asked questions
Can the root indices differ?
Use a common root index before applying this tool. It does not combine roots with different indices directly.
Are negative radicands allowed?
Yes for odd roots. Even roots of negative numbers require complex arithmetic, which this tool does not use.
Is the answer an exact simplified radical?
The combined radical is displayed, together with a floating-point approximation. Perfect-power factor extraction is not included.