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Square Root


The number k is a square root of the number n if k2 = 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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