Square Root Calculator
Free online square root calculator (radical calculator) to find the square root of any number. Calculate √x with precision and learn the mathematical principles behind square roots and radicals.
Last updated: 2025-10-21 — Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)
• Enter any positive number to calculate its square root
• Use keyboard for faster input (numbers, Enter, Esc)
• Click history items to copy results or edit
• Negative numbers are not supported (no real square root)
Our free online square root calculator (radical calculator) provides an accurate and efficient way to calculate the square root of any positive number. Whether you're a student learning about radicals and square roots, a professional working with mathematical calculations, or simply need to find the square root of a number, this radical calculator offers instant results with high precision. The square root function is fundamental in mathematics, appearing in geometry, algebra, physics, and many other fields.
Calculator Features
Discover the powerful features that make this square root calculator perfect for all your mathematical needs.
How to Use the Square Root Calculator
Learn how to effectively use our square root calculator for various types of calculations.
1. Enter Your Number
Type any positive number in the input field. You can enter integers (like 16) or decimals (like 2.25). The calculator will automatically calculate the square root.
2. View Results
The square root result will be displayed immediately. For example, √16 = 4, √25 = 5, √2.25 = 1.5. Results show both mathematical notation and decimal values.
3. Copy Results
Click the copy button to copy results to clipboard, or use keyboard shortcuts to quickly copy to other applications.
4. Try Different Numbers
Experiment with various numbers to understand how square roots work. Try perfect squares (1, 4, 9, 16, 25) and non-perfect squares (2, 3, 5, 7, 8).
5. Learn from Examples
Use the provided examples to understand mathematical concepts and see how square roots apply in real-world scenarios.
Mathematical Principles
Understanding the mathematical concepts behind square roots and their applications.
Definition of Square Root
The square root of a number x is a number y such that y² = x. For example, the square root of 16 is 4, because 4² = 16. Square roots are represented by the radical symbol √.
Perfect Squares
Perfect squares are squares of integers. Examples include 1 (1²), 4 (2²), 9 (3²), 16 (4²), 25 (5²), 36 (6²), 49 (7²), 64 (8²), 81 (9²), and 100 (10²).
Non-Perfect Squares
Numbers that are not perfect squares have irrational square roots. Examples include √2 ≈ 1.414, √3 ≈ 1.732, √5 ≈ 2.236, and √7 ≈ 2.646. These are infinite non-repeating decimals.
Properties of Square Roots
Square roots have several important properties: √(a × b) = √a × √b, √(a/b) = √a/√b (when b ≠ 0), and (√a)² = a. These properties are useful for simplifying complex expressions.
Applications in Geometry
Square roots are essential in geometry, particularly in the Pythagorean theorem (a² + b² = c²), where c = √(a² + b²). They also appear in calculating distances, areas, and volumes.
Square Root Tips and Tricks
Make the most of your square root calculations with these helpful tips.
Frequently Asked Questions
Find answers to common questions about square roots and using our calculator.
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