Master radical simplification using factors, indices, and exact forms. Review steps, graph roots, then export. Build confidence through examples, tables, and faster algebra practice.
Enter a coefficient, radicand, and root index. The calculator simplifies the radical, shows exact steps, and plots the related root curve.
This graph shows the function y = x1/n. The highlighted point uses your current radicand and root index.
| Original Expression | Prime Factorization | Simplified Form | Approximate Value |
|---|---|---|---|
| √72 | 23 × 32 | 6√2 | 8.485281 |
| 4√50 | 2 × 52 | 20√2 | 28.284271 |
| 3√54 | 2 × 33 | 33√2 | 3.779763 |
| 4√162 | 2 × 34 | 34√2 | 3.567622 |
| 3√-250 | -(2 × 53) | -53√2 | -6.299605 |
| 7√1 | 1 | 7 | 7.000000 |
Core Rule:
If a radicand can be written as an × b, then c × n√(anb) = c × a × n√b, where b has no perfect n-th power factor left.
The calculator first finds the prime factorization of the radicand. Next, it groups repeated prime factors by the root index. Full groups come outside the radical. Any leftovers stay inside.
For example, √72 = √(23 × 32). One pair of 2 and one pair of 3 leave the radical. That creates 6√2. The same idea works for cube roots, fourth roots, and higher indices.
It means removing any perfect square, cube, or higher perfect power from inside the radical. The result is an equivalent expression with the smallest possible radicand.
A complete group that matches the root index becomes one factor outside. For square roots, pairs move out. For cube roots, groups of three move out.
Yes. Enter the needed root index. The calculator groups prime factors using that index and returns the correct exact form.
Nothing moves outside the radical. The exact form stays the same because no perfect n-th power factor exists inside the radicand.
Yes, but only for odd indices like cube roots. Even roots of negative numbers are not real, so the calculator blocks those entries.
The exact answer keeps the radical form. The decimal answer gives an approximation. Both are useful for checking homework and verifying calculations.
Prime factorization reveals repeated factors clearly. That makes it easy to count full groups, extract them, and leave only unmatched factors inside.
Use CSV when you want reusable numeric data. Use PDF when you want a neat record of the exact form, factorization, and written steps.
Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.