Advanced Square Root Calculator

Calculate square roots with multiple methods, visualizations, and detailed explanations

Number to calculate square root

Enter any positive number (decimals allowed)

Select calculation precision

Calculation History

About Square Roots

The square root of a number is a value that, when multiplied by itself, gives the original number.

Notation: √x or x½

Example: √25 = 5 because 5 × 5 = 25

Property: √(a × b) = √a × √b

Common Square Roots

√1 = 1
√4 = 2
√9 = 3
√16 = 4
√25 = 5
√36 = 6
√49 = 7
√64 = 8
√81 = 9
√100 = 10
√121 = 11
√144 = 12

Calculation Methods

Method Description Accuracy Speed Best For
Newton-Raphson Iterative method using derivatives Very High Fast General use
Babylonian Ancient iterative averaging method High Fast Large numbers
Estimation Guess and check with refinement Medium Medium Educational purposes
Binary Search Divide and conquer approach High Medium Precise calculations

Square roots of negative numbers are imaginary numbers (not supported in this calculator).