Inputs
Enter a non-negative integer. We accept √, sqrt(), \\sqrt{}, commas, and full-width digits. All calculations stay in your browser.
How to use
- Enter the radicand (formats like √72 or sqrt(72) are fine).
- Keep tree/pair/approx on, set digits, and toggle bounds if you want the inequality proof.
- Scroll to visuals and steps, then export SVG or copy LaTeX for class slides.
What you’ll see
- Prime factorization (exponent form) and a compact factor tree.
- Square pairs highlighted, with inside/outside split to form a√b.
- Decimal approximation with optional k^2 < n < (k+1)^2 bounds.
- Shareable URL, LaTeX copy, and SVG export for worksheets.
Tip: teacher mode enlarges lines and contrast for projection. The “Load starter example” button immediately shows √72 → 6√2.
Results
Share & export
- Copy the URL to restore the same input and options.
- Copy LaTeX for the simplified radical and paste into notes.
- Save SVG diagrams (summary, tree, or pairing) for slides.
Factorization & visuals
Prime factors
Square bounds
Pairing view
Factor tree
Steps
FAQ
Why can pairs leave the radical?
Two of the same factor make p², and √(p²)=p. Every pair comes out; leftover singles stay inside.
What about perfect squares?
If every factor forms a pair, the inside becomes 1. √144 shows as 12 with no radical remaining.
What can I type?
Non-negative integers such as 72, √72, sqrt(72), or \\sqrt{72}. We normalize commas, spaces, and full-width digits.
How is the decimal justified?
We show the rounded decimal and the neighboring squares k² and (k+1)² so you can confirm k < √n < k+1.
Is my input sent to a server?
No. Factoring, pairing, and rendering stay in your browser.
How to use Radical Simplifier effectively
What this page is for
Use this page to simplify square roots and related radicals while keeping exact form visible. Start with the radicand and index you actually need, then compare exact and decimal forms separately.
Input checks
Check whether variables, negative values, or higher-index radicals are supported by the mode you choose. Domain assumptions affect whether a simplified expression is valid.
Workflow
A practical sequence is to factor the radicand, pull out perfect powers, review the remaining radical, and only then use a decimal approximation if needed.
Common mistakes
Avoid replacing exact radicals with decimals too early. Exact form preserves algebraic structure for later equations, proofs, or symbolic manipulation.
How to read the result
Interpret the simplified coefficient and remaining radical together. A smaller radical is not automatically a final answer if the surrounding expression still needs factoring or rationalization.
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Comments
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