How to Find Square Root of a Number

Finding the square root of a number involves a series of steps to determine the number which, when multiplied by itself, gives the original number.

Here are general rules how to find square root of a number:

Estimate a Starting Point: Start by making an educated guess or estimate of what the square root might be. For large numbers, you can use the closest perfect square to guide your estimation.
Divide the Number: Divide the original number by your estimate. This step is part of an iterative process to refine the estimate.
Calculate the Average: Find the average of the result obtained in step 2 and the estimate. This is done by adding these two numbers and then dividing by 2. This average will be a better approximation of the square root than the original estimate.
Refine the Estimate: Use the average obtained in step 3 as the new estimate.
Repeat the Process: Repeat steps 2 through 4 using the new estimate. Each repetition should bring you closer to the actual square root.
Check for Accuracy: After several iterations, check if the square is close enough to the original number. This can be done by squaring your current estimate and seeing if it is acceptably close to the original number.
Stop When Satisfied: Continue iterating until the estimate’s square is as close to the original number as needed for your purposes. The level of precision required will dictate how many iterations you need to perform.
Consider Using a Calculator for Large or Complex Numbers: For very large numbers, complex numbers, or when high precision is needed, it might be more practical to use a calculator or computer software.

Remember, this method is an iterative approach and works best with patience and practice. It’s especially useful when a precise square root is required and a calculator is not available.