SOLUTION: I still need help in trying to find out how to solve for the square root manually. I realize that with advent of calculators, this should be easy. But the prof actually wants us

Question 34892: I still need help in trying to find out how to solve for the square root manually. I realize that with advent of calculators, this should be easy. But the prof actually wants us to do it manually. Example is square root of 529. Thank you very much for your help.
Found 2 solutions by checkley71, stanbon:
Answer by checkley71(8403) (Show Source): You can put this solution on YOUR website!
ALL SQUARE ROOT NUMBERS NEED TO BE COMBINED IN SETS OF TWO COUNTING FROM THR RIGHT OF THE DECIMAL. FOR YOUR NUMBER THIS WOULD BE 5 & 29.
FINDING THE SQUARE ROOT OF THIS NUMBER IS A VARIATION ON A DIVISION STRUCTURE.
FIRST WE FIND THE LARGEST NUMBER WHEN SQUARED IS LESS THAN OR EQUAL TO 5.
THIS NUMBER IS 2. SQUARING THIS NUMBER AND SUBTRACTING (4) FROM 5 WE GET 1.
NOW WE BRING DOWN THE NEXT SET (29) AND APPEND THEM TO THE REMAINDER (1). WE
NOW HAVE 129 AND WE DOUBLE THE 2 FROM THE QUOTION (4) AND DIVIDE 129 BY 4X.
X BEING THE SECOND DIGIT IN THE NEW DIVISOR. DIVIDING THE 12 BY 4 WE GET 3.
NOW THE SECOND DIGIT IN THE QUOTION BECOMES A 3 AND THE DIVISOR NOW BECOMES
23. NOW WE MULTIPLY 3 TIMES 23 AND WE GET 129. SUBTRACTING 129 FROM 129 WE GET
A REMAINDER OF 0 AND THE ANSWER IS THE QUOTION OF 23. PROVE IT BY MULTIPLYING
23 TIMES 23.
HOPE YOU FOLLOWED THIS AS I AM NOT ABLE TO USING THE GRAPHIC/FORMULAR SYSTEM
YET.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Here is the old way:
Starting at the decimal, separate the number into packets of 2 digits:
In your case break it as follows 5 \ 29.
Find the largest perfect square less than or equal to the left-most packet.
That would be "4".
Write the square root of "4" to the left of 5\29
Divide 2 into the 5 and write the resulting 2 above the 5.
Multiply 2*2 and write the 4 below the 5.
Substract and bring down the next packet.
You now have 129 written two lines below the 529
Now it gets interesting.
Double the number written above the 529 and write 4_
(yes, that's 4_ )to the left of 129.
Now think of a digit that you can write above the
29 and to the right of the 4 in 4_ so that the product
will be as large as possible but less than 129.
That digit is "3". because 3*43=129 Whoopee!
The number above the 529 is the square root of 529
sqrt(529)=23
Cheers,
Stan H.

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