Square root

Square root

The square root, also called radiation, is an arithmetic operation, the inverse of the square of a number. The square root of any number is the number which can be multiplied by itself to yield the first number.

Any positive number, such has 9, has two square roots. Three can be multiplied by itself to yield nine, but so can negative three, because the negatives signs cancel out to yield positive 9. Any negative number has no square root, because no number multiplied by itself can be a negative number. The square root of a negative number, as the solution to an equation such as $x^{2}=-3$, is sometimes represented by $i$, imaginary.

Because all positive numbers have a negative square root as well as a positive, and in many applications only the positive in necessary (such as in geometry), the positive square root can be called the principal square root.

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