Square Root Calculator
Find the square root of any number instantly — supports decimals, perfect squares, and negative numbers
Calculate Square Root
Result
How to Use This Square Root Calculator
- Type any positive number or decimal into the input field.
- Press the Calculate Square Root button or hit Enter on your keyboard.
- The square root value, perfect square status, and detailed breakdown appear instantly.
- Click Clear to reset the calculator and enter a new number.
Key Features
Instant Results
Get the square root of any number in milliseconds with high-precision output up to 10 decimal places.
Decimal Support
Works with whole numbers, decimals, and fractions. Enter 0.25, 7.89, or 10000 with equal accuracy.
Perfect Square Detection
Automatically tells you whether the entered number is a perfect square and shows verification.
Imaginary Number Support
Handles negative numbers gracefully by returning the result in imaginary number form (e.g., 3i).
Works on All Devices
Fully responsive design that works flawlessly on mobile phones, tablets, and desktop computers.
100% Private
All calculations happen in your browser. No data is sent to any server or stored anywhere.
How Square Root Works — The Formula
The square root of a number n is a value x such that when x is multiplied by itself, the result equals n.
√ is the radical symbol. The number under the radical is called the radicand. For example, in √49, the radicand is 49, and the result is 7 because 7 × 7 = 49.
For non-perfect squares like √2, the result is an irrational number — a decimal that never terminates or repeats. The calculator provides this value to high precision.
For negative numbers, the square root involves imaginary numbers. By definition, √-1 = i (the imaginary unit). So √-16 = 4i because √16 = 4 and we multiply by i.
Practical Examples
🇮🇳 Priya — Student in Jaipur
Priya needs to find the square root of 529 for her 10th-grade math homework.
Input: 529
Calculation: √529 = 23 (because 23 × 23 = 529)
Result: 23 — Perfect square ✅
🇮🇳 Ravi — Engineer in Bengaluru
Ravi is calculating the diagonal of a square plot with area 200 sq. metres using the Pythagorean theorem.
Input: 200
Calculation: √200 = 14.1421356...
Result: 14.1421356237 — Not a perfect square
🇺🇸 Sarah — Data Analyst in Chicago
Sarah needs the square root of 0.0625 for a standard deviation calculation in her dataset.
Input: 0.0625
Calculation: √0.0625 = 0.25 (because 0.25 × 0.25 = 0.0625)
Result: 0.25 — Perfect square ✅
🇮🇳 Amit — Physics Student in Delhi
Amit encounters √-36 in a quadratic equation with complex roots.
Input: -36
Calculation: √-36 = √36 × √-1 = 6i
Result: 6i — Imaginary number
What Is a Square Root?
A square root is one of the most fundamental operations in mathematics. When you calculate the square root of a number, you are finding a value that, when multiplied by itself, produces the original number. The concept dates back thousands of years — ancient Babylonians were computing square roots on clay tablets around 1800 BCE.
Square roots appear everywhere in real life: calculating distances (Pythagorean theorem), determining standard deviation in statistics, computing area and dimensions in architecture, and even in financial formulas like the Sharpe ratio. If you have studied physics, you have seen square roots in kinematic equations, wave frequencies, and gravitational formulas.
Understanding whether a number is a perfect square matters in number theory, cryptography, and competitive exams. This calculator not only gives you the value but also tells you whether the number is a perfect square, shows the verification, and handles edge cases like zero, decimals, and negative numbers.
Square Root in Multiple Languages
📖 Want to learn more about square roots, their properties, and real-world applications?
Read Our Complete Guide to Square Roots →Frequently Asked Questions
Is this square root calculator free to use?
Yes, this square root calculator is completely free with no signup, no limits, and no hidden charges. Use it as many times as you need.
Can I calculate the square root of decimal numbers?
Absolutely. Enter any decimal number like 2.5, 0.04, or 123.456 and the calculator will return the precise square root.
What is a perfect square?
A perfect square is a number whose square root is a whole integer. For example, 4, 9, 16, 25, 36, 49, 64, 81, and 100 are all perfect squares.
Can I find the square root of negative numbers?
Square roots of negative numbers result in imaginary numbers. This calculator handles negative inputs by showing the result in imaginary form (e.g., √-4 = 2i).
How accurate is this square root calculator?
The calculator uses JavaScript's built-in Math.sqrt() function which provides results accurate to 15 significant digits, which is more than sufficient for any practical use.
What is the square root of 2?
The square root of 2 is approximately 1.41421356. It is an irrational number, meaning its decimal expansion goes on forever without repeating.
How is square root different from cube root?
A square root finds a number that when multiplied by itself gives the original number (√9 = 3 because 3×3 = 9). A cube root finds a number that when multiplied by itself three times gives the original number (∛27 = 3 because 3×3×3 = 27).
Can I use this calculator on my phone?
Yes, the calculator is fully responsive and works perfectly on smartphones, tablets, and desktop computers across all modern browsers.
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