Posted by Kiera on Tuesday, February 26, 2008 at 10:39pm.
In my case, I use a hand calculator. Before they existed, I used a log table or a slide rule. There is a pencil-and-paper way to calculate square roots that are not integers, but it is rather complicated. Almost no one teaches it anymore. If that is what you want, I may be able to find you a reference.
In the meantime: sqrt(42) = 6.481..
sqrt(84) = 9.165..
I would love you to teach me the method because i am not sure if state tests will ask for that.
There is an example of the method us "oldtimers" had to learn as students, and which I taught to my students before calculators were available.
http://www.homeschoolmath.net/teaching/square-root-algorithm.php
Go about one page down on the site to where it says
"Finding a square root using an algorithm"
and see if you can follow their example.
To attempt to explain it here and show it here is a bit too complicated.
Here is another example using a larger number.
The nice thing about this method is that it gives you the exact decimals up to your point of progress in the solution.
Also it will work for the calculation of square roots of decimals, but you have to start the initial pairing of digits from the decimal point, pairing them going to both the left and the right of the decimal
http://www.homeschoolmath.net/teaching/square-root-algorithm-example.php