How to Find Square Root of a Non Perfect Square
Finding the square root of a non perfect square can be a challenging task, especially if you’re not familiar with the various methods available. However, with the right techniques, you can easily determine the square root of any number, even if it’s not a perfect square. In this article, we will explore several methods to help you find the square root of a non perfect square.
1. Estimation Method
The estimation method is a simple and straightforward approach to finding the square root of a non perfect square. It involves approximating the square root by finding two numbers that, when multiplied together, are closest to the given number.
To use this method, follow these steps:
1. Find two numbers, a and b, such that a^2 < number < b^2. 2. Calculate the average of a and b: (a + b) / 2. 3. Check if the square of this average is equal to the given number. If not, adjust the average by adding or subtracting 1 from it and repeat the process until you find a number whose square is closest to the given number.
2. Long Division Method
The long division method is a more precise way to find the square root of a non perfect square. It involves dividing the given number by a series of numbers that are close to the square root.
Here’s how to use the long division method:
1. Write the given number under the long division symbol.
2. Find the largest integer whose square is less than or equal to the given number. Write this integer as the first digit of the square root.
3. Subtract the square of this integer from the given number and bring down the next digit.
4. Double the first digit of the square root and append it to the right of the number you just brought down.
5. Divide the resulting number by the doubled digit and write the quotient below the division symbol.
6. Repeat steps 3-5 until you have found the square root to the desired accuracy.
3. Newton’s Method
Newton’s method, also known as the Newton-Raphson method, is an iterative method for finding successively better approximations to the roots (or zeroes) of a real-valued function. It can be used to find the square root of a non perfect square by following these steps:
1. Start with an initial guess for the square root, let’s call it x0.
2. Calculate the square of x0: x0^2.
3. Subtract x0^2 from the given number: number – x0^2.
4. Divide the result by 2×0: (number – x0^2) / (2×0).
5. Update the guess for the square root: x1 = x0 – (number – x0^2) / (2×0).
6. Repeat steps 2-5 until the difference between x1 and x0 is less than a desired tolerance.
By using these methods, you can easily find the square root of a non perfect square. Whether you prefer the simplicity of the estimation method, the precision of the long division method, or the iterative nature of Newton’s method, you’ll be able to determine the square root of any number with confidence.
