Radical Multiplication Calculator
Multiply mixed-index radicals by converting to fractional exponents. Simplifies products like square root times cube root.
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About
Multiplying radicals with the same index is straightforward (√a × √b = √ab), but students often struggle when indices differ, such as multiplying a square root by a cube root. This tool handles these "mixed-index" cases by converting radicals into rational exponents.
The utility finds the Least Common Multiple (LCM) of the indices to unify the radicals under a single root, then simplifies the radicand by extracting perfect powers. This ensures the answer is in its simplest radical form.
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Formulas
The process involves three steps: Exponent conversion, Common Denominator (Index), and Radical reconstruction.
{
n√a = a1nxan ⋅ xbm = x(am+bnnm)
Reference Data
| Expression | Exponent Form | Common Index | Result |
|---|---|---|---|
| √2 × √3 | 21/2 × 31/2 | 2 | √6 |
| √2 × 3√2 | 21/2 × 21/3 | 6 | 6√32 |
| √x × √x | x1/2 × x1/2 | 2 | x |
Frequently Asked Questions
No. 2 * sqrt(3) is simply 2sqrt(3). You cannot bring the 2 inside unless you square it first: sqrt(4) * sqrt(3) = sqrt(12).
If indices match, sqrt(a) * sqrt(b) = sqrt(ab). This works for any non-negative real numbers.