πŸ”’Free Online Calculators

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 β€” Compiled and reviewed by Calvin (Math Research, FreeCalculators.app)

√
Click buttons to input
Click AC to clear

β€’ Enter any positive number to calculate its square root

β€’ Use keyboard for faster input (numbers, Enter, Esc)

β€’ Click history items to copy results or edit

β€’ 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.

βœ“Calculate square root of any positive number
βœ“High precision decimal results
βœ“Support for both integers and decimal numbers
βœ“Instant calculation with real-time results
βœ“Copy results to clipboard with one click
βœ“Responsive design for all devices
βœ“Keyboard input support for faster calculations
βœ“Clear error handling for invalid inputs
βœ“Mathematical notation display (√x)
βœ“Educational examples and explanations

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 (1Β²), 4 (2Β²), 9 (3Β²), 16 (4Β²), 25 (5Β²), 36 (6Β²), 49 (7Β²), 64 (8Β²), 81 (9Β²), and 100 (10Β²).

Non-Perfect Squares

Numbers that are not perfect squares have irrational square roots. Examples include √2 β‰ˆ 1.414, √3 β‰ˆ 1.732, √5 β‰ˆ 2.236, and √7 β‰ˆ 2.646. These are infinite non-repeating decimals.

Properties of Square Roots

Square roots have several important properties: √(a Γ— b) = √a Γ— √b, √(a/b) = √a/√b (when b β‰  0), and (√a)Β² = 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.

1.Memorize perfect squares up to 15Β² (225) for quick mental calculations
2.For non-perfect squares, use estimation: √50 is between √49 (7) and √64 (8), so approximately 7.07
3.When dealing with large numbers, factor them: √(100 Γ— 25) = √100 Γ— √25 = 10 Γ— 5 = 50
4.Use the calculator to verify your mental math and build confidence
5.Practice with both perfect squares and non-perfect squares to understand the difference
6.Remember that negative numbers don't have real square roots (they are imaginary)
7.For decimals, square roots are also decimals: √0.25 = 0.5
8.Use square roots to solve quadratic equations and other algebraic problems
9.In real-world applications, square roots often represent distances, ratios, or scaling factors
10.The square root function is the inverse of the squaring function: if x² = y, then x = ±√y

Frequently Asked Questions

Find answers to common questions about square roots and using our calculator.

Related Calculators

View all calculators β†’
πŸ”’

Basic Calculator

Perform essential math operations for daily calculations. Perfect for homework, budgeting, and quick calculations.

Try it now
πŸ“Š

Percentage Calculator

Free percentage calculator. Quickly find percentage increase, decrease, change, or what percent of a number another number is. Easy & accurate.

Try it now
⬜βšͺ

Area Calculator

Calculate the area of seven common shapes: rectangle, triangle, trapezoid, circle, sector, ellipse, and parallelogram. Perfect for geometry, construction, and land measurement.

Try it now