How to Calculate Square Root of Non Perfect Squares
Calculating the square root of non perfect squares can sometimes be a challenging task, especially if you’re not familiar with the various methods available. Non perfect squares are numbers that do not have an exact square root that can be expressed as a whole number. In this article, we will explore several methods to calculate the square root of non perfect squares, including approximation techniques and the use of mathematical tools.
One of the simplest methods to approximate the square root of a non perfect square is the long division method. This method involves dividing the number by the largest possible square number until the remainder is smaller than the divisor. For example, to find the square root of 17, you would divide 17 by 16 (which is the largest square number less than 17), resulting in a quotient of 1 and a remainder of 1. You would then continue this process with the remainder, dividing by the next largest square number (which is 4) and so on. This method can be time-consuming, but it provides a good approximation of the square root.
Another method for approximating the square root of a non perfect square is the Newton-Raphson method. This method is an iterative process that starts with an initial guess for the square root and then refines the guess by repeatedly applying a formula. The formula for the Newton-Raphson method is:
x_n+1 = (x_n + n/x_n) / 2
where x_n is the current guess for the square root and n is the number whose square root you want to find. By repeatedly applying this formula, you can converge on a more accurate approximation of the square root.
In addition to these approximation methods, you can also use a calculator or a computer program to find the square root of a non perfect square. Most calculators have a built-in square root function that can provide an exact value for any real number. Similarly, computer programs such as Microsoft Excel or Google Sheets can also calculate the square root of a non perfect square using the SQRT function.
It’s important to note that while these methods can provide approximations or exact values for the square root of non perfect squares, they may not always yield a perfect result. This is because non perfect squares do not have an exact square root that can be expressed as a whole number or a simple fraction. However, by using these methods, you can find a value that is as close as possible to the true square root.
In conclusion, calculating the square root of non perfect squares can be achieved through various methods, including the long division method, Newton-Raphson method, and the use of calculators or computer programs. Each method has its own advantages and limitations, but with a bit of practice, you can become proficient in finding the square root of any non perfect square.
