Square Root Calculator
Find the square root of any non-negative number with this free online calculator. It computes the principal square root, tells you whether the number is a perfect square, and provides the simplified radical form for integer inputs.
The square root of a number x is a value y such that y x y = x. For example, the square root of 25 is 5, because 5 x 5 = 25. The symbol for square root is the radical sign.
Key Concepts:
- Principal Square Root: Every positive number has two square roots (one positive, one negative), but the principal square root is the positive one. For example, sqrt(9) = 3, not -3.
- Perfect Squares: A number is a perfect square if its square root is an integer. Examples: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100.
- Simplified Radical Form: A radical expression is simplified when no perfect square factor remains under the radical sign. For example, sqrt(72) = sqrt(36 x 2) = 6 x sqrt(2).
- Imaginary Numbers: The square root of a negative number is not a real number. In the complex number system, sqrt(-1) is defined as i (the imaginary unit).
Square roots appear in geometry (Pythagorean theorem, distance formula), physics (energy equations, wave mechanics), statistics (standard deviation), and many other fields.