Input
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.
Result
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.
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Comments
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