What is the symbol for square root?

The symbol for the square root is called a radical sign (√).

What is the square root of 2?

The square root of 2 is an irrational number, approximately equal to 1.41421356. It cannot be expressed as a simple fraction.

Calculate the Square Root

The Square Root Calculator provides a quick and easy way to find the square root of any number. The square root of a number 'x' is a number 'y' such that y² = x. For example, the square root of 9 is 3 because 3² = 9. Simply enter a number to find its square root instantly.

Square Root Calculator

Calculate the square root of any positive number. This calculator supports both perfect and non-perfect squares, providing detailed results including decimal approximations and simplified radical forms where applicable.

Input Value

Number:

Display Options

Decimal Places:

Show calculation steps

Show simplified radical form

About Square Roots

A square root of a number is a value that, when multiplied by itself, gives the original number. Every positive number has two square roots: one positive (principal square root) and one negative. By convention, the square root symbol (√) refers to the positive square root.

Key Concepts

Perfect Squares: Numbers whose square roots are integers (e.g., 4, 9, 16, 25).
Irrational Square Roots: Square roots of non-perfect squares result in irrational numbers (e.g., √2, √3).
Principal Square Root: The positive square root of a number, denoted by √.
Simplified Radical Form: Expressing square roots in their simplest form by factoring out perfect squares.

Properties of Square Roots

√(a × b) = √a × √b
√(a/b) = √a / √b (where b ≠ 0)
√a² = |a| (absolute value of a)
(√a)² = a (for a ≥ 0)
√0 = 0
√1 = 1

Applications

Square roots are fundamental in mathematics and have numerous practical applications:

Geometry: Calculating distances and dimensions using the Pythagorean theorem
Physics: Determining velocities, accelerations, and wave frequencies
Statistics: Computing standard deviations and variance
Engineering: Analyzing electrical circuits and structural loads
Finance: Calculating volatility and risk metrics
Computer Graphics: Distance calculations and vector normalization

Square Root Calculator Overview

The Square Root Calculator is a simple and interactive tool that helps users find the square root of any positive number. It can handle both perfect squares (like 16 or 25) and non-perfect squares (like 2 or 7), providing exact values or decimal approximations as needed. This makes it a useful companion for students, teachers, and professionals who need quick and accurate results in mathematics, science, or finance.

Formula:

√x = y where y² = x

This means that the square root of a number (x) is another number (y) which, when multiplied by itself, equals the original number. For example, √16 = 4 because 4 × 4 = 16.

How to Use the Calculator

The calculator is designed for ease of use, whether you are verifying your math homework or performing a quick scientific check. Follow these steps to get your result:

Step 1: Enter a positive number in the input box.
Step 2: Choose how many decimal places you want in your result.
Step 3: (Optional) Check or uncheck options to show calculation steps or simplified radical form.
Step 4: Click the Calculate button to view the result instantly.
Step 5: Press Reset to start a new calculation.

Understanding the Results

Once you calculate, the tool presents several helpful details:

Square Root Value: The main result, shown as either an exact value or a decimal approximation.
Original Number: The number you entered for reference.
Verification: Confirms the result by squaring the calculated root.
Perfect Square Check: Tells you whether the number is a perfect square.
Simplified Radical Form: Displays the square root in its simplest radical expression, such as √50 = 5√2.
Step-by-Step Breakdown: Shows how the result was determined, ideal for learning and review.

Why This Calculator Is Useful

The Square Root Calculator saves time and reduces manual calculation errors. It’s particularly valuable for:

Students: Learning about square roots, perfect squares, and radical simplifications.
Teachers: Demonstrating step-by-step mathematical procedures clearly.
Scientists and Engineers: Computing square roots in physics, geometry, and technical formulas.
Financial Analysts: Estimating risk, volatility, and statistical measures.

By displaying both approximate decimal values and simplified radical forms, the calculator bridges the gap between theoretical understanding and practical application.

Frequently Asked Questions (FAQ)

What is a square root?

A square root is a number that produces a specified value when multiplied by itself. For example, the square root of 9 is 3 because 3 × 3 = 9.

Can I use negative numbers?

No. This calculator only works with non-negative numbers. The square roots of negative numbers are called complex numbers and are not handled by this tool.

What does “simplified radical form” mean?

Simplified radical form expresses a square root by factoring out perfect squares. For example, √72 can be simplified to 6√2.

What is a perfect square?

A perfect square is a number that is the square of an integer, such as 1, 4, 9, 16, 25, and so on.

Can I control the precision of the result?

Yes. You can select how many decimal places you want your result to display—ranging from 0 up to 10 digits—for more detailed or rounded outputs.

Conclusion

The Square Root Calculator combines mathematical accuracy with user-friendly interaction. It provides instant results, educational explanations, and practical value across various fields. Whether you are studying, teaching, or solving technical problems, this calculator helps make mathematical reasoning faster and clearer.

More Information

Understanding Square Roots:

Perfect Squares: Numbers whose square root is a whole number (e.g., √4 = 2, √81 = 9).
Non-Perfect Squares: Numbers whose square root is an irrational number (a decimal that goes on forever without repeating), e.g., √2 ≈ 1.414...
Negative Numbers: The square root of a negative number is an imaginary number, involving the unit 'i', where i = √-1. For example, √-16 = 4i.

Our calculator can handle all of these cases.

Frequently Asked Questions

What is a square root?: The square root of a number is a value that, when multiplied by itself, gives the original number. Every positive number has two square roots: a positive one and a negative one.
What is the symbol for square root?: The symbol for the square root is called a radical sign (√).
What is the square root of 2?: The square root of 2 is an irrational number, approximately equal to 1.41421356. It cannot be expressed as a simple fraction.

About Us

We create basic, reliable math tools for everyday use. Our calculators are designed to be fast, accurate, and straightforward, providing instant answers for common mathematical operations.