HOW TO FIND SQUARE ROOTS WITH OUT A CALCULATOR

FIND SQUARE AND CUBE ROOTS WITHOUT A CALCULATOR
When I was in algebra last year they told me to fined square root I need a calculator or root chart, so I thought there must be a way to do in in your head or on paper.  When I googled it I found some extremely complicated 15 step proses of which the example number was 5 digits long.  I found a sequence that goes along with square roots.  A square minus the previous square equals a number in the sequence.  1-0=1, 4-1=3, 9-4=5, 16-9=7 and so on.  The sequence is 1,3,5,7,9 and so on.  To find the square root of 16 subtract 1 then 3 then 5 and so on until you get to 0.  The add up the number of numbers you subtracted and that is the square root.  16-1-3-5-7=0.  1,3,5,7 is 4 numbers in the sequence; therefore the square root is 4.  Lets try 5.  5-1-3 we get 2 with 1 left over that's not right.  5-1-3-5 we get 3 with 4 left over that's also not right.  5-1-3-1/5 5=0.  The first 2 digits of the root are 2.2 or 2 1/5.  Try it your self.  The same trick works for cube or any other kind of root.  For cube use the sequence 1,7,19,45,80 and so on.  For tet[tetracube] roots use 1,15,66 and so on.
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