Square root

A square root of a number is a value that squares to that number. For nonnegative real numbers, the principal square root is the nonnegative root.

Exponentiation: The operation of raising a number to a power, including repeated multiplication by itself. A square root reverses exponentiation by the power of two.
Inverse function: A function that reverses another function on a domain where that function is one-to-one. Squaring is not one-to-one over all real numbers, so a restricted domain is needed for inversion.
Pythagorean theorem: A theorem stating that the squares of a right triangle’s legs sum to the square of its hypotenuse. Finding a side length from the other two requires taking a square root.
Cube root: A number that, when raised to the third power, equals a given number. Unlike real square roots, real cube roots exist for negative inputs and retain their sign.
Real number: A number on the continuous number line, including rational and irrational values. Real numbers contain the principal square roots of all nonnegative real numbers.
Quadratic equation: An equation whose highest power of the unknown is two. Solving x² = a requires considering both square roots when a is positive.
Euclidean distance: The straight-line distance between points, calculated from the sum of squared coordinate differences. The distance formula takes the square root of a sum of squared differences.
Nth root: A number that raised to an integer power n equals a specified number. Square roots are the second-root case, with special sign and multiplicity rules.
Complex number: A number of the form a + bi, where a and b are real and i² = −1. Negative real numbers have square roots only after the number system is extended to complex numbers.
Principal value: A conventionally selected value among multiple values associated with a mathematical operation. The principal square root chooses the nonnegative value from the two real roots of a positive number.

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