Square Root of 8 - MathQuadrum

What is square root of 8? Let’s explore the exact steps how to find square root of a number based on the below example

Estimate a Starting Point: Begin with an estimate. For 8, a good starting point might be 2 or 3, as the square root will be between these two numbers (since 2²=4 and since 3²=9)
Divide the Number: Divide 8 by your estimate. For instance, if you start with 2.5, you would calculate 8 : 2.5.
Calculate the Average: Find the average of the result from step 2 and your initial estimate. This is done by adding the two numbers and dividing by 2.
Refine the Estimate: Use the average obtained in step 3 as your new estimate.
Repeat the Process: Repeat steps 2 through 4 using the new estimate. With each iteration, your estimate should become a closer approximation of the square root of 8.
Check for Accuracy: After each iteration, check the accuracy of your estimate. You can do this by squaring your current estimate. If the square is close to 8, your estimate is accurate.
Continue Until Satisfied: Keep iterating until your estimate squared is as close to 8 as you need it to be. The number of iterations will depend on how precise you want the estimate to be.
Note on Precision: For most practical purposes, a few iterations will yield a sufficiently precise estimate. However, for more exact requirements, you may need additional iterations.

General rules: How to Find Square Root of a Number

Practical examples: