Radicals and Exponents Calculator
Simplify roots and convert radicals to fractional exponents. Factorizes radicands to find perfect squares.
Simplified Form:
Decimal Approximation:
Prime Factors:
About
Simplifying radicals is a staple of algebra, often required before adding or subtracting surds. This tool decomposes the number inside the root (the radicand) into prime factors to identify perfect squares. It pulls perfect squares out from under the radical sign to produce the simplest radical form. Additionally, it bridges the gap between radical notation and exponent notation, which is essential for calculus and higher-level function analysis.
radicals
roots
surds
simplification
algebra
Formulas
The simplification relies on the property of roots regarding products:
√a × b = √a × √b
If a factor is a perfect square (k2), it is moved outside:
√k2x = k√x
Reference Data
| Input Radical | Prime Factors | Simplification | Exponent Form |
|---|---|---|---|
| √8 | 2, 2, 2 | 2√2 | 81/2 |
| √12 | 2, 2, 3 | 2√3 | 121/2 |
| √18 | 2, 3, 3 | 3√2 | 181/2 |
| √75 | 3, 5, 5 | 5√3 | 751/2 |
Frequently Asked Questions
This specific tool is optimized for square roots (index 2). The logic looks for pairs of prime factors. Cube roots would require finding triplets, which is a similar but distinct process.
Decimals are approximations. In math and engineering, keeping exact values like square root of 2 ensures no precision is lost during intermediate steps of a calculation.