Square root

In mathematics, the principal square root of a non-negative real number x,! is denoted sqrt x and represents the non-negative real number whose square (the result of multiplying the number by itself) is x,!.

Related Topics:
Mathematics - Non-negative - Real number

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For example, sqrt 9 = 3 since 32 = 3 × 3 = 9.

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This example suggests how square roots can arise when solving quadratic equations such as x^2=9 or, more generally, ax^2+bx+c=0.

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There are two solutions to the square root of a non-zero number. For a positive real number, the two square roots are the principle square root and the negative square root. For negative real numbers, the concept of imaginary and complex numbers has been developed to provide a mathematical framework to deal with the results.

Related Topics:
Imaginary - Complex number

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Square roots of positive integers are often irrational numbers, i.e., numbers not expressible as a quotient of two integers. For example, sqrt 2 cannot be written exactly as m/n, where n and m are integers. Nonetheless, it is exactly the length of the diagonal of a square with side length 1.

Related Topics:
Integer - Irrational number - Quotient - Diagonal - Square

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The discovery that sqrt 2 is irrational is attributed to Hippasus, a disciple of Pythagoras.

Related Topics:
Hippasus - Pythagoras

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The square root symbol (√) was first used during the 16th century. It has been suggested that it originated as an altered form of lowercase r, representing the Latin radix (meaning "root").

Related Topics:
Symbol - 16th century - R - Latin - Root

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