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.
Faktorisasi & visual
Prime factors
Square bounds
Tampilan pasangan
Pohon faktor
Langkah
FAQ
Mengapa pasangan bisa keluar dari akar?
Dua faktor sama membentuk p² dan √(p²)=p. Setiap pasangan keluar; faktor tunggal tetap di bawah akar.
Bagaimana dengan kuadrat sempurna?
Jika semua faktor berpasangan, bagian dalam menjadi 1 dan √144 ditulis 12 tanpa akar.
Apa saja yang bisa diinput?
Bilangan bulat tak negatif seperti 72, √72, sqrt(72), atau \\sqrt{72}. Koma, spasi, dan digit fullwidth dinormalisasi.
Bagaimana dasar pendekatan desimalnya?
Kami tampilkan desimal yang dibulatkan dan kuadrat tetangga k² serta (k+1)² agar jelas k < √n < k+1.
Apakah input dikirim ke server?
Tidak. Faktorisasi, pasangan, dan visual dibuat di peramban Anda.
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