Skip to main content

Square Root Calculator : Calculate & Simplify Radicals (√x)

The Calcivo Square Root Calculator computes the principal positive square root (√x) for any real number. In addition to high-precision decimal outputs, it extracts square factors to provide the exact simplified radical form (e.g. √72 = 6√2).

Interactive Calculator

100% Client-Side Engine
√
Principal Square Root (√72)
8.485281
Exact Simplified Radical
6√2
Perfect Square Check
No (Irrational Radical)
Radical Simplification Steps
1. Principal square root: √72 = 8.485281
2. Simplified radical form: 6√2

Step-by-Step Examples

Simplifying Square Root of 72 (√72)

Simplifying radical to exact mathematical form.

Inputs: Radicand (x): 72
Result: 8.485281 (Simplified: 6√2)

72 = 36 × 2. Since √36 = 6, √72 = √(36 × 2) = 6√2.

How to Use This Tool

  1. Enter a positive real number inside the radicand.
  2. Click Calculate to solve the square root.
  3. Review the decimal result, simplified radical form, and perfect square verification.

Frequently Asked Questions

A perfect square is an integer whose square root is an exact whole integer (e.g. √49 = 7). An irrational square root has a non-terminating, non-repeating decimal expansion (e.g. √2 ≈ 1.414213...).