what is the square root of 43
The correct answer and explanation is:
The square root of 43 is approximately 6.557.
To explain how to find the square root of a number, consider that the square root of a number is a value that, when multiplied by itself, gives the original number. In this case, the square root of 43 is the number that, when squared, equals 43.
Since 43 is not a perfect square (like 16 or 25), the square root cannot be expressed as an integer. This means it is an irrational number, which cannot be written as a simple fraction and has a non-repeating, non-terminating decimal expansion. The square root of 43 lies between 6 and 7 because 6² = 36 and 7² = 49.
To estimate the square root of 43 more precisely, one can use methods such as the Newton-Raphson method or a calculator. Using a calculator, the square root of 43 gives approximately 6.557. This value can be rounded depending on the desired level of precision.
For a deeper understanding, square roots are commonly used in various fields, such as geometry, where they are essential in calculating distances in the Cartesian plane, and in algebra, where they appear in quadratic equations. The concept of square roots also has applications in physics, engineering, and statistics, such as when determining standard deviations or working with quadratic functions.
In summary, the square root of 43 is approximately 6.557, and its value cannot be expressed as a simple fraction because it is an irrational number.