√ Square Root Calculator - Free Online √x Calculator | Math Tools
Free online square root calculator to find the square root of any number. Calculate √x with precision and learn the mathematical principles behind square roots.
• 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 provides an accurate and efficient way to calculate the square root of any positive number. Whether you're a student learning about radicals, a professional working with mathematical calculations, or simply need to find the square root of a number, this 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 use our square root calculator effectively for various types of calculations.
1. Enter Your Number
Type any positive number into the input field. You can enter integers (like 16) or decimal numbers (like 2.25). The calculator will automatically calculate the square root.
2. View the Result
The square root result will be displayed instantly. For example, √16 = 4, √25 = 5, √2.25 = 1.5. The result shows both the mathematical notation and the decimal value.
3. Copy the Result
Click the copy button to copy the result to your clipboard, or use keyboard shortcuts for quick copying to use in 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 the mathematical concepts and see how square roots are applied 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. The square root is denoted by the radical symbol √.
Perfect Squares
Perfect squares are numbers that are the square 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 decimal numbers that continue infinitely without repeating.
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 & 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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