math ToolUpdated 2026-09-19
Square Root Calculator
Calculate the principal square root and cube root of any positive number.
Formula & Mathematical Methodology
√x = x^(1/2)
The square root of a number is a value that, when multiplied by itself, gives the original number.
How to Use This Square Root Calculator
- Enter a positive number.
- Click Calculate to see the square root and cube root.
Step-by-Step Worked Example
Scenario: √144
1. Identify factor pair: 12 × 12 = 144
2. Principal square root is 12
Final Calculated Result: 12
What Does Your Result Mean?
Represents the side length of a square whose area equals the input number.
Common Practical Applications:
- Pythagorean theorem hypotenuse calculation
- Geometry and quadratic formulas
- Electrical impedance
Important Limitations & Assumptions:
- Real square roots cannot be extracted from negative numbers.
Frequently Asked Questions
What is a perfect square?
A perfect square is an integer whose square root is a whole integer (e.g., 4, 9, 16, 25, 144).
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