Square Root of 5 - MathQuadrum

What is square root of 5? Let’s explore the exact steps how to find square root of a number based on the below example

Choose an Initial Estimate: Start with an estimate for the square root. For 5, a reasonable starting point might be 2, since 2²=4 and since 3²=9, so the square root of 5 is somewhere between 2 and 3.
Divide the Number by the Estimate: Divide 5 by your initial estimate. For instance, if you start with 2, calculate 5 : 2 = 2.5
Calculate the Average: Find the average of the result from the previous step and your estimate. This means adding your initial estimate (2) to the result (2.5) and then dividing by 2, giving (2+2.5) : 2 = 2.25.
Use the Average as a New Estimate: Take the average calculated in step 3 and use it as your new estimate.
Repeat the Process: Repeat steps 2 through 4 using the new estimate. In this case, divide 5 by 2.25 and then average the result with 2.25.
Check for Accuracy: After a few iterations, check the accuracy of your estimate by squaring it. If the square of your estimate is close to 5, it means you have a good approximation.
Continue Iterating Until Satisfied: Continue the process until the squared estimate is as close to 5 as you need. The number of iterations will depend on the desired level of precision.
Conclude with the Best Estimate: Once you’ve reached an acceptable level of accuracy, the estimate you have is the square root of 5 to the precision you’ve calculated.

General rules: How to Find Square Root of a Number

Practical examples: