Factor Radicals Calculator

Outside Coefficient	Index	Radicand	Variable Part	Simplified Result
3	2	72	None	18√2
2	3	54	None	6∛2
1	4	80	x⁶	2x · ⁴√5x²
-5	3	-16	y⁷	10y² · ∛(2y)

Formula Used

Numeric factoring: If N = aⁿ × b, then ⁿ√N = a × ⁿ√b.

Variable factoring: If m = qn + r, then ⁿ√(x^m) = x^q × ⁿ√(x^r).

Even-index caution: For even roots, extracting x^qn gives |x|^q unless the variable is assumed nonnegative.

The calculator finds the largest perfect nth-power factor inside the radical, moves it outside, leaves the remainder inside, and then multiplies everything by the outside coefficient.

How to Use This Calculator

Enter the outside coefficient already multiplying the radical.
Set the radical index, such as 2 for square root or 3 for cube root.
Type the integer radicand you want to factor.
Add an optional variable symbol and exponent for algebraic radicals.
If needed, enter a variable value to get a decimal approximation.
Choose whether the variable should be treated as nonnegative.
Press Factor Radical to see the simplified form above the form.
Use the CSV or PDF buttons to export your result.

FAQs

1. What does factoring radicals mean?

It means pulling perfect powers out of a radical. For example, √72 becomes √(36×2), which simplifies to 6√2.

2. Can this calculator handle cube roots and higher indices?

Yes. Enter any index from 2 through 12. The calculator groups prime factors according to that index and simplifies the radical correctly.

3. Why do absolute value bars appear sometimes?

They appear with even roots when a variable factor leaves the radical. That is because √(x²) equals |x|, not always x.

4. What if the radicand is zero?

Any radical with zero inside becomes zero. The calculator reports zero immediately and skips unnecessary factorization steps.

5. Can I use decimals for exact factoring?

Use decimals for the outside coefficient and optional variable value. Keep the radicand and exponents as integers for exact symbolic simplification.

6. Does it show an approximate decimal value?

Yes. If the expression is fully numeric, or if you provide a variable value, the calculator returns a decimal approximation using your chosen precision.

7. What does the remainder under the radical mean?

The remainder contains factors that cannot form a complete group matching the index. Those factors must stay inside the radical after simplification.

8. Can I export my result?

Yes. After calculating, use the CSV button for spreadsheet-friendly output or the PDF button for a clean printable summary.

Calculator Form

Example Data Table