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Without calculator? If you have a lot of time and using just pencil and paper, you can use a method called "Newton's Method". But it's very cumbersome and laborious. I would say it would take you about an hour to find square root of 35 to 10 decimal places.Scary, ha!!.
Sep 24, 2015 1:47:10 AM+5
moderator #2 CPhill
Here's a method to do this....it's called "divide and average".....the goal is to get two results that are very close to each other......
Let's try 35.....we know the square root has to be between 5 and 6 so let's take the average of these two numbers = [5 + 6] / 2 = 5.5
Divide 35 by this 35/5.5 = about 6.36 this is too big
Now take the average of the last two results [ 5.5 + 6.36[/ 2 = 5.93
Divide 35 by this = 5.9021922428330523 too small
Average the last two results again [5.93 + 5.9021922428330523]/2 = 5.91609612141652615
Divide 35 by this = 5.9160634448278270072
If we do this one more time, we should have something rhat's pretty accurate
[5.91609612141652615 + 5.9160634448278270072] / 2 = 5.9160797831221765786
Divide 35 by this = 5.9160797830770555065347
Which is extremely close to our last result.....!!!!
Note that the onsite calculator gives the value of sqrt(35) = 5.916079783099616
Which is very close to ours !!!
There are other methods available, but I like this one the best......!!!!
Sep 24, 2015 2:02:07 AM
edited by CPhill Sep 24, 2015 2:10:05 AM
