This alternative square root formula states that the square root of a number is a number raised to the exponent of the fraction one-half: There is also another common notation of square roots that could be more convenient in many complex calculations. It is because √0 = 0, and zero is neither positive nor negative. The only number that has one square root is zero. However, for many practical purposes, we usually use the positive one. Each positive real number always has two square roots – the first is positive, and the second is negative. Where ⟺ is a mathematical symbol that means if and only if. Therefore, the square root formula can be expressed as: The square root of a given number x is every number y whose square y² = y × y yields the original number x. In this article, we will focus on the square root definition only. Nonetheless, we sometimes add to this list some more advanced operations and manipulations: square roots, exponents, logarithms, and even trigonometric functions (e.g., sine and cosine). In mathematics, the traditional operations on numbers are addition, subtraction, multiplication, and division. Thus, the word radical doesn't mean far-reaching or extreme, but instead foundational, reaching the root cause. x is called a root or radical because it is the hidden base of a. The last question is, why is the square root operation called root regardless of its true origin? The explanation should become more evident if we write the equation x = ⁿ√a in a different form: xⁿ = a. The notation of the higher degrees of a root has been suggested by Albert Girard, who placed the degree index within the opening of the radical sign, e.g., ³√ or ⁴√. Although the radical symbol with vinculum is now in everyday use, we usually omit this overline in many texts, like in articles on the internet. The "bar" is known as a vinculum in Latin, meaning bond. The first use of the square root symbol √ didn't include the horizontal "bar" over the numbers inside the square root (or radical) symbol, √‾.
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