Calculation result
Step-by-step work
Merged result
A text copy downloads automatically five seconds after calculation.
Calculator inputs
Formula used
Fractional exponents follow \(a^{m/n}=\sqrt[n]{a^m}\). This identity connects exponential and radical forms.
Product rules use \(\sqrt[n]{a}\sqrt[n]{b}=\sqrt[n]{ab}\). Denominator rationalisation uses matching powers or conjugates.
Equation candidates are checked in the original expression. This final check removes extraneous solutions before reporting them.
How to use
Select the required mode first. Enter values using the labelled fields. Choose real or complex numbers when needed.
Set decimal precision before calculating. Review exact forms, decimal values, restrictions, and steps. Invalid entries produce specific correction messages.
Use the export buttons after calculation. Results remain available in local browser history. Check every equation answer against its original form.
Example data
| Mode | Input | Expected result |
|---|---|---|
| Simplify radical | √72 | 6√2 |
| Exponent to radical | x^(3/4) | ⁴√(x³) |
| Radical to exponent | ⁵√(x²) | x^(2/5) |
| Add radicals | 2√8 + 3√18 | 13√2 |
| Rationalise | 1/√3 | √3/3 |
| Solve equation | √(x + 5) = 4 | x = 11 |
Calculation history
Frequently asked questions
What is radical form?
Radical form uses a root symbol instead of a fractional exponent. Both forms describe the same mathematical value.
How does the calculator simplify radicals?
It extracts perfect-power factors from the radicand. The remaining factor stays inside the radical.
Can it simplify cube roots?
Yes. Choose a root index of three. Custom positive integer indices are also supported.
Does it support negative radicands?
Odd roots support negative radicands in real mode. Complex mode also handles many even-root cases.
What does rationalising a denominator mean?
It removes radicals from a denominator. The calculator uses matching factors or a conjugate.
Can unlike radicals be added?
Unlike radicals cannot combine into one radical term. Their decimal sum can still be evaluated.
Why can radical equations create extraneous answers?
Squaring both sides can introduce false solutions. Every proposed answer must satisfy the original equation.
What is the principal root?
The principal root is the standard nonnegative root. Equation mode can still report multiple valid solutions.
Can I export results?
Yes. Copy the merged result, download CSV data, or print the page as a PDF.