# Square Root

### imaginary negative symbol

The number *k* is a square root of the number *n* if *k*^{2} = *n*. For example, 4 and -4 are the square roots of 16 since 4 × 4 = 16 and (-4) × (-4) = 16. The square root symbol is √ and for *n* greater than **zero**, the symbol is understood to be a **positive number**. Thus √ 16 = 4 and -√ 16 = -4.

When *n* is a negative number, the square root √n is called *imaginary*. Customarily, √-1 is designated by *i* so that the square root of any negative number can be expressed as *ai* where *a* is a real number. Thus √-5 = 5 *i*.

See also Imaginary number.

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