How to Find Square Root of Non Perfect Square
Finding the square root of a non-perfect square can be a challenging task, especially for those who are not familiar with mathematical concepts. However, with the right techniques and tools, it is possible to determine the square root of any number, even if it is not a perfect square. In this article, we will explore various methods to find the square root of a non-perfect square.
1. Long Division Method
The long division method is a traditional technique that can be used to find the square root of a non-perfect square. To use this method, follow these steps:
1. Write the number whose square root you want to find.
2. Draw a vertical line to the right of the number.
3. Find the largest perfect square that is less than or equal to the number.
4. Write the square root of this perfect square above the vertical line.
5. Multiply the square root by itself and write the result below the number.
6. Subtract the result from the number.
7. Bring down the next digit of the number.
8. Repeat steps 4 to 7 until you have found the square root.
2. Bisection Method
The bisection method is an efficient technique that can be used to find the square root of a non-perfect square. This method involves repeatedly dividing the interval containing the square root in half until the desired level of accuracy is achieved. Here are the steps to follow:
1. Choose a number that is greater than the square root of the non-perfect square.
2. Divide this number by 2 to get a new estimate.
3. Square the new estimate and compare it to the non-perfect square.
4. If the squared estimate is greater than the non-perfect square, subtract the estimate from the original number and repeat step 2.
5. If the squared estimate is less than the non-perfect square, add the estimate to the original number and repeat step 2.
6. Continue this process until the difference between the squared estimate and the non-perfect square is within the desired level of accuracy.
3. Newton’s Method
Newton’s method, also known as the Newton-Raphson method, is an iterative technique that can be used to find the square root of a non-perfect square. This method involves approximating the square root by repeatedly refining an initial guess. Here’s how to use Newton’s method:
1. Choose an initial guess for the square root.
2. Calculate the square of the guess.
3. Subtract the squared guess from the non-perfect square.
4. Divide the result by twice the guess.
5. Add the result to the guess to get a new estimate.
6. Repeat steps 2 to 5 until the difference between the squared estimate and the non-perfect square is within the desired level of accuracy.
4. Using a Calculator
If you are looking for a quick and easy way to find the square root of a non-perfect square, using a calculator is the best option. Modern calculators have built-in functions that can calculate the square root of any number, including non-perfect squares. Simply enter the number, press the square root button, and the calculator will provide the result.
In conclusion, finding the square root of a non-perfect square can be achieved using various methods, such as the long division method, bisection method, Newton’s method, or a calculator. By understanding these techniques, you can easily determine the square root of any number, regardless of whether it is a perfect square or not.
