Square Root Calculator
The square root function finds a number that, when multiplied by itself, equals the input value. This calculator computes the square root of any positive real number, providing instant and accurate results for mathematical, scientific, and engineering applications.
Popular Calculations
Mathematical Explanation
The square root of a number x, denoted √x, is a value that, when multiplied by itself, gives x. For example, √9 = 3 because 3 × 3 = 9. Square roots are the inverse operation of squaring a number. For positive numbers, there are two square roots (positive and negative), but this calculator returns the principal (positive) square root.
Frequently Asked Questions
A square root of a number is a value that, when multiplied by itself, equals the original number. For example, the square root of 16 is 4 because 4 × 4 = 16.
In real numbers, you cannot find the square root of a negative number. However, in complex numbers, the square root of negative numbers involves imaginary numbers (using i, where i² = -1).
A perfect square is a number whose square root is a whole number. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, and 100. For instance, √16 = 4 (exactly).
The square root of 0 is 0: √0 = 0. This is because 0 × 0 = 0.
The square root symbol is √, called a radical sign. The expression √x means "the square root of x." This symbol has been used in mathematics since the 16th century.
Resources & References
Encyclopedia Resources
- Square Root - Wikipedia - Comprehensive guide to square roots and their properties
- Nth Root - Wikipedia - Learn about roots and radical expressions
Educational Resources
- Khan Academy - Square Roots - Free square root lessons and practice problems
- Math is Fun - Square Root - Interactive square root examples and explanations