Friendly Surds The Problem:
Square roots of most
numbers are irrational � infinitely long strings of non-recurring decimal
digits, with no discernible pattern to them.
Sometimes, however, you
find rather strange things happening� Try adding
together. Then square this new
number. What have you accidentally
found the value of? So,
, for some integer value N. Now try finding what
give you the value of. Can you make up your
own combination of �friendly� surds that behave like this? You can use more than two
surds, or subtraction instead of addition�
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