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,!.

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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.

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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.

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

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Non-negative: REDIRECT negative and non-negative numbers...

Real number: In mathematics, the real numbers are intuitively defined as numbers that are in one-to-one correspondence with the points on an infinite line—the number line. The term "real number" is a retronym coined in response to "imaginary number"....

Imaginary: This is a disambiguation page ? a navigational aid which lists other pages that might otherwise share the same title. If an article link referred you here, you might want to go back and fix it to point directly to the intended page....

Square root related Images and Photos (experimental)

Square One	Square No. 19	Time Square	Root Vue Farm
Square by Square Puzzle	Times Square	Times Square	Apple Square
Times Square	Yellow Square	Times Square I	Hanover Square