Calculate square roots instantly with our free online calculator. Find perfect squares, simplify radicals, and see step-by-step solutions. Puro client-side, no ads.
The square root of a number is a value that, when multiplied by itself, gives the original number. For example, the square root of 16 is 4 because 4 × 4 = 16. This calculator handles all non-negative real numbers, identifies perfect squares, simplifies radical expressions, and provides precise decimal approximations. All calculations happen instantly in your browser.
The square root of a number x is a number y such that y² = x. For example, √9 = 3 because 3² = 9. Every positive number has two square roots — one positive and one negative — but by convention we usually refer a the principal (positive) square root.
A perfect square is a number that is the square of an integer. Examples include 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, and so on. The square root of a perfect square is always an integer.
Not among real numbers. The square root of a negative number is an imaginary number, denoted with i (where i = √-1). For example, √-9 = 3i. Real-world square root calculations typically only work with non-negative numbers.
The calculator finds the largest perfect square factor of the input number and factors it out. For example, √50 = √(25 × 2) = √25 × √2 = 5√2. This is the simplified radical form.
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