🔢 Square Root Calculator
Compute square roots with high precision using Newton‑Raphson, Babylonian, binary search, or the native Math.sqrt. Compare methods, see convergence steps, and adjust decimal places.
Step 1: Number & Settings
6
20
💡 About precision
Decimal places determine how many digits after the decimal point are shown. More iterations allow methods to converge closer to the true value, especially for large numbers.
Step 2: Algorithm
10–10
📐 How it works
Newton & Babylonian use iteration xₙ₊₁ = 0.5·(xₙ + S/xₙ). Binary search halves an interval. Tolerance 10⁻ⁿ stops when change is below that value.
Square Root Result
Summary
Method Comparison
Step‑by‑Step
√x =
5.000000
(native method, 6 decimal places)
Number (x)
25
√x (exact to precision)
5.000000
Method
native
Tolerance
1e-10
⚖️ Method comparison
| Method | Result | Error (vs native) | Iterations used |
|---|
📉 Convergence steps (selected method)
📝 Iteration details
Select a method and compute to see step‑by‑step approximation.
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