Posted by sapna on Tuesday, December 18, 2012 at 8:05am.
Are you suggesting a "pencil-and-paper" method?
I will show you three ways.
1.
This is what I taught years ago, before we had calculators
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
look at the method labeled "algorithm"
2.
You could also use Newton's Method
-start with a reasonable guess
I guess 20
-divide 404.41 by 20 to get 20.22505
average that answer with my guess
(20 + 20.22505)/2 = 20.11025 ---> new guess
make that your new guess and repeat:
404.41รท20.11025 = 20.109645..
(20.109645+20.11025)/2 = 20.10994779 --> new guess
404.41/20.10994779 = 20.10994778
(20.10994779+20.10994778)/2 = 20.10994779 --> the same as before
so √404.41 = 20.10994799 correct to 8 decimal places in 3 steps
If you start with a silly guess, like 10 , eventually you will get the answer, it will just take longer.
3.
of course you could also just do :
√404.41 = 20.10994779 on your calculator.