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Square Root Calculator

Square Root Calculator — get the answer instantly in your browser, free and private.

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About the Square Root Calculator

A free in-browser square root calculator that instantly finds the principal square root of any positive real number without sign-up or data uploads. Simply enter a number and get precise results in milliseconds. Perfect for students learning algebra, professionals verifying calculations, and anyone needing quick square root solutions for everyday math problems.

How Square Root works

A square root calculator works by finding the number that, when multiplied by itself, equals your input. Mathematically, if you want to find the square root of n, you are solving for x where x * x = n, written as sqrt(n) = x.

Worked Example:

Find the square root of 144.
Formula: sqrt(144) = x, where x * x = 144
Calculation: 12 * 12 = 144
Result: sqrt(144) = 12

Another example with a non-perfect square:
Find sqrt(10)
Calculation: 3.162 * 3.162 = 9.9987 (approximately 10)
Result: sqrt(10) = 3.162 (rounded to three decimal places)

The calculator uses efficient numerical algorithms to compute the exact square root instantly, even for very large numbers or decimals.

How to use

  1. Enter your values as shown in the input box.
  2. The result is calculated instantly.
  3. Click Copy to use it.

Common uses

  • Verify perfect squares quickly (identify that 49 = 7 squared, 100 = 10 squared)
  • Calculate side lengths of squares when you know the area - for example, a square room with 225 square feet has sides of 15 feet
  • Solve algebra equations and word problems that require finding square roots
  • Check homework answers without a scientific calculator or calculator app
  • Understand mathematical relationships in geometry, physics, and engineering applications

Frequently asked questions

What is a square root?
A square root is the number that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 times 4 equals 16. Every positive number has exactly one positive square root (called the principal square root).
Can this calculator handle decimal numbers?
Yes, this calculator works with any positive real number, including decimals. For example, it can find sqrt(2.5) = 1.581 or sqrt(0.64) = 0.8.
What is a perfect square?
A perfect square is a whole number whose square root is also a whole number. Examples include 4, 9, 16, 25, 36, 49, 64, 81, and 100. The calculator identifies these instantly.
Why do I need a square root calculator if my phone has one?
This browser-based tool is faster to access than opening an app, works across all devices without download or installation, requires no sign-up or account, and keeps your calculations private with nothing stored or uploaded.
How accurate are the results?
The calculator provides results accurate to many decimal places. For perfect squares, results are exact. For non-perfect squares, the calculator computes decimal approximations using standard numerical algorithms.
Can I calculate negative square roots?
The principal square root of any positive number is always positive. Negative numbers do not have real square roots in standard mathematics. If you need advanced complex number calculations, use a scientific calculator or math software.