Radical Expression Simplifier
Simplify square roots and cubic roots by extracting perfect squares/cubes. Transforms radicals into their simplest mixed form.
About
Radical simplification involves rewriting a root expression so that the number inside the radical (the radicand) has no factors that are perfect powers of the index. For example, the square root of 75 is not in simplest form because 75 contains the factor 25, which is a perfect square. The simplified form is 5 multiplied by the square root of 3.
This tool performs prime factorization on the radicand to identify and extract these perfect powers. It supports square roots (index 2) and cubic roots (index 3). This process is critical in algebra and geometry for finding exact values rather than decimal approximations.
Formulas
The property used for simplification is:
If a is a perfect square (k2), then:
Reference Data
| Radical | Factors | Perfect Square | Simplification |
|---|---|---|---|
| √8 | 2 × 2 × 2 | 4 | 2√2 |
| √12 | 4 × 3 | 4 | 2√3 |
| √75 | 25 × 3 | 25 | 5√3 |
| √18 | 9 × 2 | 9 | 3√2 |