Square Root Calculator

The square root of a nonnegative number is a value that produces the original number when multiplied by itself. This square root calculator finds the principal, or nonnegative, square root and displays a precise decimal answer. It works with whole numbers and decimals and identifies when an integer input is a perfect square. Students can use it to check arithmetic, while professionals can use it for geometry, engineering, statistics, finance, and any formula involving a squared quantity. For example, the square root of 144 is 12 because 12 multiplied by 12 equals 144. The number 144 is called a perfect square because its principal square root is an integer. The square root of 2 is not an integer or a terminating decimal. It is an irrational number whose decimal digits continue without repeating, so the calculator shows a rounded approximation. Calculations retain the available floating-point precision before the display is rounded. Every positive number technically has two values that solve an equation of the form x squared equals n: one positive and one negative. For 25, both 5 and negative 5 square to 25. However, the square root symbol conventionally means the principal nonnegative root, so the calculator returns 5. When solving equations, remember to consider both positive and negative solutions if the context requires them. Zero is a special case whose square root is exactly zero. Negative real numbers do not have real square roots because multiplying two real numbers with the same sign always gives a nonnegative product. Complex mathematics defines the imaginary unit as the square root of negative one, allowing roots of negative values to be expressed with imaginary numbers. This calculator focuses on real square roots and therefore asks for a value greater than or equal to zero. Square roots reverse squaring and appear throughout mathematics. The Pythagorean theorem uses a square root to convert a sum of squared lengths into a distance. Standard deviation takes the square root of variance so the result returns to the original unit. Area formulas use square roots to recover a side length from a square area. Roots also appear in quadratic formulas, growth models, electrical calculations, and computer graphics. To verify any displayed result, multiply it by itself and compare the product with the original input; the calculator includes that check directly beneath the answer.