CalculatorHandy

Math Calculators

Square Root Calculator

Find the square root of any number, or choose another root such as a cube root. For whole numbers, the calculator also gives the simplified radical form and tells you whether the number is a perfect power.

Square root of 728.48528137424
Simplified radical
6√2
Perfect square?
No
Step-by-step working
  1. Find the largest perfect square factor: 72 = 36 × 2
  2. Take its root outside: √36 = 6, so √72 = 6√2
  3. Decimal value = 8.48528137424; check: 8.4852813742 ≈ 72

How to use the Square Root Calculator

  1. Enter the number.
  2. Keep 2 for a square root or choose another root degree.
  3. Press Calculate.

Formula

ⁿ√x = x1/n. To simplify √72, split it into a perfect square times the rest: √(36 × 2) = 6√2.

Examples

  • √144 = 12 (a perfect square).
  • √72 = 6√2 ≈ 8.485281.
  • ∛−125 = −5.

Frequently asked questions

Does a number have two square roots?

Yes: 9 has square roots 3 and −3. Calculators return the principal (non-negative) root, 3.

Related calculators