Square Root Calculator (√n)
√n with integer-perfect-square check, simplified surd form, and decimal expansion.
Result
√n
7.071068
Simplified surd: 5√2.
- n50
- Decimal7.0710678119
- Perfect square?No
- Simplified surd5√2
- n²2500
Step-by-step
- Decimal: √50 = 7.07106781.
- Surd simplification: extract largest k² that divides n. Result: 5√2.
How to use this calculator
- Enter non-negative number.
- Read decimal + simplified surd form.
About this calculator
The square root of n is the value x where x² = n. Perfect squares (1, 4, 9, 16, 25, …) have integer roots; everything else has irrational roots. Simplified surd form pulls out the largest perfect-square factor: √50 = √(25 × 2) = 5√2. JavaScript Math.sqrt is implementation-defined but typically uses hardware FPU instruction (CVTSS2SS, FSQRT) — accurate to last bit. For huge integers, Newton's method or arbitrary-precision libraries.
Frequently asked
Cleaner exact representation. √50 = 5√2 — easier to reason about than 7.0710678…
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