The square root of a number is a value that, when multiplied by itself, gives the original number. In the case of 64, we can break it down to see why 8 is the square root. The number 64 can be expressed as 8 × 8, which makes it clear that 8 is indeed the square root of 64.
The concept of square roots dates back to ancient civilizations. The Babylonians had methods for approximating square roots, and their tablet, known as YBC 7289, is believed to be one of the earliest mathematical artifacts discussing square roots. They used a form of the method of averaging that resembles modern techniques.
In mathematical terms, the square root is denoted with the radical symbol (√). Therefore, we write it as √64 = 8. The value 8 is the principal square root of 64, which is the positive value. However, every positive number also has a negative counterpart; thus, -8 is also a square root of 64 in a broader mathematical context.
Understanding square roots is essential, particularly in algebra and geometry. They are crucial in solving equations, particularly quadratic equations, where the roots (solutions) are represented using square roots. For example, in the quadratic equation x² - 64 = 0, finding the roots involves taking the square roots of both sides, leading to x = ±8.
Square roots also have practical applications in various fields, including engineering, physics, and computer science. For example, in statistics, the standard deviation, a measure of how spread out numbers are in a data set, is calculated using the square root. This can help in understanding the dispersion of data in randomized trials or experimental outcomes.
In summary, the square root of 64 is 8, which can be verified through multiplication or the application of algebraic principles. Additionally, it's fascinating how the concept of square roots has evolved over time and its continued importance in modern mathematics and applied sciences.