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The mathematical expression 'The (principal) square root of x' In, a square root of a number a is a number y such that y 2 = a; in other words, a number y whose (the result of multiplying the number by itself, or y⋅ y) is a. For example, 4 and −4 are square roots of 16 because 4 2 = (−4) 2 = 16. Every nonnegative a has a unique nonnegative square root, called the principal square root, which is denoted by √ a, where √ is called the or radix. For example, the principal square root of 9 is 3, which is denoted by √ 9 = 3, because 3 2 = 3 • 3 = 9 and 3 is nonnegative. The term (or number) whose square root is being considered is known as the radicand. The radicand is the number or expression underneath the radical sign, in this example 9.
Every positive number a has two square roots: √ a, which is positive, and − √ a, which is negative. Together, these two roots are denoted as ± √ a (see ).
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Although the principal square root of a positive number is only one of its two square roots, the designation ' the square root' is often used to refer to the principal square root. For positive a, the principal square root can also be written in notation, as a 1/2. Square roots of negative numbers can be discussed within the framework of. More generally, square roots can be considered in any context in which a notion of 'squaring' of some mathematical objects is defined (including,, etc.).
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Contents • • • • • • • • • • • • • • • • • • • • History [ ] The clay tablet was created between 1800 BC and 1600 C, showing √ 2 and √ 2/2 = 1/ √ 2 as 1;24,51,10 and 0;42,25,35 base 60 numbers on a square crossed by two diagonals. The is a copy from 1650 BC of an earlier and other texts – possibly the – that shows how the Egyptians extracted square roots by an inverse proportion method. In, the knowledge of theoretical and applied aspects of square and square root was at least as old as the, dated around 800–500 BC (possibly much earlier).