What is a Square Root?

A square root of a number x is a number y such that y² = x. In other words, it's the number that when multiplied by itself gives the original number. For example, the square root of 64 is 8 because 8 × 8 = 64. The square root symbol is √ (radical symbol).

Formula: √x = y where y × y = x

Examples: √64 = 8 | √144 = 12 | √2 ≈ 1.4142

How to Use This Calculator

Enter any number (positive, negative, decimal, or zero) in the input field
Click "Calculate Square Root" or press Enter
View the square root result with step-by-step explanation
Check if the number is a perfect square (integer square root)

Understanding Your Results

Square root result: The principal (positive) square root of your number
Perfect square? Indicates if your number is a perfect square (has an integer square root)
Rounded result: Square root rounded to 4 decimal places for easy reference
Negative numbers: Square roots of negative numbers are imaginary numbers (displayed with i)

Common Square Roots (Perfect Squares)

Perfect Squares Reference

√1 = 1√4 = 2√9 = 3√16 = 4√25 = 5√36 = 6 √49 = 7√64 = 8√81 = 9√100 = 10√121 = 11√144 = 12 √169 = 13√196 = 14√225 = 15√256 = 16√289 = 17√324 = 18 √361 = 19√400 = 20√441 = 21√484 = 22√529 = 23√576 = 24

Why Use Our Square Root Calculator?

✅ 100% Free — No hidden fees or subscriptions
✅ No Registration — Use instantly without creating an account
✅ Accurate — High precision calculations with up to 15 decimal places
✅ Handles negatives — Shows imaginary numbers for negative inputs
✅ Step-by-step explanation — Understand how the result is derived
✅ Mobile friendly — Works perfectly on any device

Applications of Square Roots

📐 Geometry: Calculate side lengths of squares and right triangles
📊 Statistics: Standard deviation and variance calculations
🏗️ Engineering: Structural calculations and formulas
💰 Finance: Volatility calculations and risk assessment
🔬 Physics: Velocity, acceleration, and energy formulas
🎓 Education: Algebra, calculus, and advanced mathematics

Frequently Asked Questions

What is the square root of 0? — √0 = 0, because 0 × 0 = 0.
Can I take the square root of a negative number? — Yes! The square root of a negative number is an imaginary number (e.g., √-4 = 2i).
What is a perfect square? — A perfect square is a number whose square root is a whole number (e.g., 16, 25, 36).
What is the square root of 2? — √2 ≈ 1.41421356... (an irrational number).
What's the difference between square root and square? — Square (x²) multiplies a number by itself; square root (√x) finds the number that when squared gives x.

Square Root Calculator