Calculator inputs
Choose one operation and enter each radical carefully. Use fractions or decimals when needed. The calculator validates every submitted value before solving.
Quick examples
Load a prepared example with one click. Change any value before calculating. Each example demonstrates a different radical rule clearly.
Calculation history
Formula used
The calculator factors each numerical radicand first. Complete exponent groups move outside the root. Remaining factors stay inside for an exact result.
How to use
- Select the required calculation mode.
- Enter the root index from two through twelve.
- Provide each coefficient, radicand fraction, and variable factor.
- Choose real or complex output rules.
- Select rationalisation, detailed steps, and decimal precision.
- Submit the form and review every result panel.
- Copy, print, or export the merged solution.
Worked examples
| Expression | Factoring idea | Simplified result |
|---|---|---|
| √72 | 72 = 2³ × 3² | 6√2 |
| ∛432 | 432 = 2⁴ × 3³ | 6∛2 |
| √(72x³) | 72x³ = 36x² × 2x | 6|x|√(2x) |
| ∛(54a⁷b⁴) | 54a⁷b⁴ = 27a⁶b³ × 2ab | 3a²b∛(2ab) |
Common mistakes
Do not split sums across a radical. Extract only complete perfect-power groups. Remember absolute values for even roots of variables.
Frequently asked questions
What does factoring a radical mean?
It means decomposing the radicand into useful factors. Perfect powers can then leave the radical. Other factors remain inside unchanged.
Can this calculator simplify cube roots?
Yes, choose an index of three. The solver extracts every perfect cube. It also handles variables with grouped exponents.
Can I enter a fraction?
Yes, use separate numerator and denominator fields. Each field also accepts decimal values. Mixed numbers like 1 1/2 are supported.
Why do absolute values appear?
Even roots return non-negative principal values. Therefore √(x²) equals |x| generally. Select positive variables to remove that notation.
Can negative radicands be calculated?
Odd roots accept negative radicands directly. Even roots need complex-number mode. The result then uses the principal complex root.
How are like radicals added?
Both operands are simplified before comparison. Matching radical parts share one coefficient. Different radical parts remain separate terms.
What does rationalising mean?
Rationalising removes a radical from a denominator. An equivalent radical factor is introduced. Ordinary factors are then reduced normally.
Why might decimal output be unavailable?
Variables do not have assigned numerical values. Exact symbolic output remains fully valid. Substitute numbers first for a decimal estimate.
Can I export the full solution?
Yes, copy the merged result directly. Download its fields as a CSV file. Use printing to save a PDF copy.