SOLUTION: Is it possible to find the square root of a number that is not a perfect square without a calculator? Such as 80? 195? etc...

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Question 75410: Is it possible to find the square root of a number that is not a perfect square without a calculator? Such as 80? 195? etc...
Found 2 solutions by stanbon, checkley75:
Answer by stanbon(75887) (Show Source):
You can put this solution on YOUR website!
Such a numberis irrational which means its decimal form is a non-repeating
pattern.
You can never write the entire decimal form but you can carry it out
to as many places as you have the patience to do so.
---------
For example:
sqrt 80 = ?
8 8.9 8.94 8.944 8.9442 ----------
If you square 8.9442 you will find it is less than 80
If you square 9 you will find it is more than 80.
So the square root is in between 8.9442 and 9.
You can keep this up forever if you wish.
----------
Cheers,
Stan H.

Answer by checkley75(3666) (Show Source):
You can put this solution on YOUR website!
YES BUT IT IS MESSY:
&&&&&&&&&8.944 IS THE SQRT OF 80
&&&&&&&&&--------------
&&&&&&8)80.000000
&&&&&&&)64 DOUBLE THE 8 & ADD THE 9
------------------------
xxxx169)1600
XXXXXXXX1521
--------------------------
&&&&&1784)7900 DOUBLE THE 89 & ADD THE 4
&&&&&&&&&&7136
-----------------------
&&&&&17884)76400 DOUBLE THE 894 & ADD THE 4
&&&&&&&&&&&71536
----------------------
&&&&&&&&&&&&4864