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Square (algebra)
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<p>In <a href="/facts/Mathematics/pxTouaz4">mathematics</a>, a square is the result of <a href="/facts/Multiplication/VtcUjpNv">multiplying</a> a <a href="/facts/Number/auQSAE2m">number</a> by itself. The verb "to square" is used to denote this operation. Squaring is the same as <a href="/facts/Exponentiation/pac6QY2g">raising to</a> the power <a href="/facts/2_(number)/u5WC44t9">2</a>, and is denoted by a <a href="/facts/Superscript/6tExBnkw">superscript</a> 2; for instance, the square of 3 may be written as 32, which is the number 9. In some cases when superscripts are not available, as for instance in <a href="/facts/Programming_language/cWTYbgWa">programming languages</a> or <a href="/facts/Plain_text/TSlSSAg2">plain text</a> files, the notations <i>x</i>^2 (<a href="/facts/Caret/LRV5MF7s">caret</a>) or <i>x</i>**2 may be used in place of <i>x</i>2. The adjective which corresponds to squaring is <i>quadratic</i>. </p><p>The square of an <a href="/facts/Integer/PUwwrawx">integer</a> may also be called a <i><a href="/facts/Square_number/jfakASPK">square number</a></i> or a <i>perfect square</i>. In <a href="/facts/Algebra/nMdqczjo">algebra</a>, the operation of squaring is often generalized to <a href="/facts/Polynomial/Lzak8VVx">polynomials</a>, other <a href="/facts/Expression_(mathematics)/MPrMlYbE">expressions</a>, or values in systems of mathematical values other than the numbers. For instance, the square of the <a href="/facts/Linear_function_(calculus)/sbyEbb6x">linear polynomial</a> <i>x</i> + 1 is the <a href="/facts/Quadratic_polynomial/mKxHIC3U">quadratic polynomial</a> (<i>x</i> + 1)2 = <i>x</i>2 + 2<i>x</i> + 1. </p><p>One of the important properties of squaring, for numbers as well as in many other mathematical systems, is that (for all numbers x), the square of x is the same as the square of its <a href="/facts/Additive_inverse/n8gKUmCf">additive inverse</a> −<i>x</i>. That is, the square function satisfies the identity <i>x</i>2 = (−<i>x</i>)2. This can also be expressed by saying that the square function is an <a href="/facts/Even_function/tGHWJqAa">even function</a>. </p>