Square Root Calculator
Professional-grade calculator with step-by-step explanations
Enter your number in the input field on the left, then click the "Calculate √" button. Your result will appear on the right with detailed step-by-step calculations below. Use the copy button to copy results, as they may be longer than displayed.
Calculation History
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Square Root Tutorial
What is a Square Root?
A square root of a number x is a value that, when multiplied by itself, gives x. For example, √9 = 3 because 3 × 3 = 9.
Perfect Squares
Numbers like 1, 4, 9, 16, 25, 36... are perfect squares because their square roots are whole numbers (1, 2, 3, 4, 5, 6...).
Irrational Numbers
Most square roots (like √2, √3, √5) are irrational numbers with infinite, non-repeating decimal expansions.
Historical Facts
The Radical Symbol (√)
The radical symbol √ was first used in print by German mathematician Christoph Rudolff in 1525 in his book "Coss".
Ancient Origins
The concept of square roots dates back to ancient Babylonians around 2000 BCE. They used geometric methods and approximation techniques.
Greek Mathematics
Ancient Greeks discovered that √2 is irrational, leading to a crisis in their mathematical philosophy that only accepted rational numbers.
Advanced Features
Copy Functionality
Click any copy button to copy results to clipboard. Useful for long decimal results.
Multiple Methods
View different calculation approaches including Newton's method and prime factorization.
Detailed Analysis
Get comprehensive information about mathematical properties and convergence analysis.
Feature | Details |
---|---|
Price | Free |
Rendering | Client-Side Rendering |
Language | JavaScript |
Paywall | No |
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