Calculator
This version treats “MC” as mixed-coefficient mode. Enter a coefficient, an integer root, a constant under the radical, and an exponent on x.
Formula Used
Write the expression as c × n√(a × xp).
Factor the constant so a = bn × r, where r has no complete nth-power group.
Split the variable power as xp = xnq+s = xnq × xs.
Then the simplified form becomes c × b × xq × n√(r × xs).
For even roots, standard classroom simplification assumes x ≥ 0.
How to Use This Calculator
- Enter the coefficient outside the radical.
- Choose the root index, such as 2 or 3.
- Type the integer constant under the radical.
- Enter the exponent attached to x inside the radical.
- Set a sample x value for a numeric verification.
- Choose graph limits and the graph step size.
- Press Simplify Radical to show the answer above the form.
- Download the result summary as CSV or PDF if needed.
Example Data Table
| Original Expression | Simplified Result |
|---|---|
| 2√(72x5) | 12x2√(2x) |
| 33√(54x7) | 9x23√(2x) |
| √(50x3) | 5x√(2x) |
| 4√(18x6) | 12x3√(2) |
| 54√(16x9) | 10x24√(x) |
FAQs
1) What does this calculator simplify?
It simplifies radicals like 2√(72x5) or 33√(54x7). The tool extracts perfect powers, moves full x groups outside, and leaves only unsimplified terms inside the radical.
2) Does the calculator assume x is positive?
Yes for even roots. Pulling x2 from √(x2) is shown as x here, which follows the common classroom assumption x ≥ 0. Odd roots do not need that assumption.
3) Can it handle cube roots and fourth roots?
Yes. Enter the root index you want. The same extraction logic works for square roots, cube roots, fourth roots, and higher integer roots up to 10.
4) What if nothing comes out of the radical?
Then the expression is already simplified for the chosen root. The result section will still show the original form, the status label, and a numeric verification.
5) Why does the input use integer constants and exponents?
Exact radical simplification depends on prime factor groups and modular exponent splitting. Integer inputs keep the algebra exact and make the displayed steps easy to verify by hand.
6) Why do the two graph lines overlap?
They should overlap wherever the expression is real because the simplified expression is algebraically equivalent to the original one. The graph helps confirm that equivalence visually.
7) Can I export my result?
Yes. Use the CSV button for spreadsheet-style review or the PDF button for a printable summary of the current calculation, numeric check, and simplification details.
8) Is this a full symbolic algebra system?
No. It focuses on structured radical simplification with an integer constant and a power of x. That makes it fast, clear, and useful for classroom-style work.