Square Root Calculator

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What Is a Square Root?

The square root of a number is the value that, when multiplied by itself, gives the original number. The square root of 25 is 5, because 5 times 5 equals 25. Square roots are the inverse operation of squaring a number, just as division is the inverse of multiplication.

Perfect squares (1, 4, 9, 16, 25, 36, 49, 64, 81, 100...) have whole number square roots. The square roots of all other positive integers are irrational numbers, meaning they cannot be expressed as a simple fraction and their decimal expansions go on forever without repeating.

Cube Roots and Higher

The cube root of a number is the value that, when cubed (multiplied by itself twice), gives the original number. The cube root of 27 is 3, because 3 times 3 times 3 equals 27. Unlike square roots, cube roots of negative numbers are real and negative: the cube root of -8 is -2.

Square Roots in Real Life

Square roots appear in the Pythagorean theorem (finding the length of a hypotenuse), in the quadratic formula (solving second-degree equations), in standard deviation calculations (taking the square root of variance), in physics (the relationship between distance and time for free-falling objects), and in determining the side length of a square when you know its area.