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Approximating Square Roots
To approximate square roots you need to find which "nice" square roots the radical lies.  etc... Notice the list of square roots all simplify to the integers 1, 2, 3, 4, 5, and 6. If you are trying to find the  you need to find out what it is in between! 
 falls in between  and 
If you simplify each radical you get that  falls in between 5 and 6.
Now you must approximate the decimal. Half way in between 25 and 36 is 30.5, 27 is less than 30.5 so  is less than 5.5. In fact,  is fairly close to  so it is approximately 5.2 
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