<\/span><\/h2>\nTo find the value of the square root of 5, let’s walk through the following steps:<\/p>\n
Step 1:<\/strong> Start by making an initial guess. Since 5 is between 4 and 9, it makes sense to choose a value between the square roots of these two perfect squares. Let’s take the average of 4 and 9, which is 6.5. This can serve as our initial guess.<\/p>\nStep 2:<\/strong> Divide the number whose square root we are finding (in this case, 5) by the initial guess we made in Step 1. So 5\/6.5 = 0.7692307692.<\/p>\nStep 3:<\/strong> Take the average of the initial guess and the result of the division in Step 2. (6.5 + 0.7692307692)\/2 = 3.6346153846. This result becomes our revised guess.<\/p>\nStep 4:<\/strong> Repeat Step 2 and Step 3, using the revised guess in place of the initial guess, until you reach a desired level of accuracy. In this case, let’s repeat the process one more time.<\/p>\n – 5\/3.6346153846 = 1.374419075<\/p>\n
– (3.6346153846 + 1.374419075)\/2 = 2.50401723<\/p>\n
Step 5:<\/strong> Continue this iterative process until you are satisfied with the level of accuracy. After a few more repetitions, we find that the value converges to approximately 2.2360679775.<\/p>\n