If you
don’t have an electronic
calculator, you can extract
square
roots arithmetically as follows:
Suppose you want to
extract the square root of
2,034.01.
First, divide
the number
into two-digit
groups, working away from the
decimal point. Set off
this way the number appears as:
Next, find
the largest number
whose square can be contained
in
the first group, This
is the number
4, whose square is 16. The 4 is the first digit
of
your answer. Place the
4 above the
20, and
place its square
(16) under the first
group, thus:
Now perform
the indicated
subtraction and bring down
the next group to the
right, thus:
Next, double the
portion of the answer already found (4, which doubled is 8), and set the
result down as
the first digit of a
new divisor, thus:
The
second
digit of the new
divisor is obtained by a trial-and-error method. Divide
the single
digit 8 into the
first
two digits of the remainder
434 (that is, into 43) until you obtain the largest
number that you can (a) add as another digit to
the divisor and (b)
use as a
multiplier which, when
multiplied by the increased
divisor, will produce
the largest result containable
in the remainder 434. In
this case, the first number
you try is 43 + 8, or 5.
Write this 5 after the 8 and
you
get
85. Multiply 85 by 5
and
you get 425, which is
containable in 434.
The second digit of
your answer is therefore 5. Place
the 5
above 34. Your
computation
will now
look like this:
Proceed
as
before to perform the
indicated subtraction and bring down the next group,
thus:
Again
double the
portion of
the answer already found, and set the result (45 x 2, or
90) down as the first
two digits of a new divisor thus:
Proceed as
before to determine
the largest number that can be added as a digit to
the divisor 90 and used
as a multiplier which, when
multiplied by
the increased divisor,
will produce a result
containable
in the remainder, 901. This number is
obviously 1. The
increased divisor is 901, and this
figure,
multiplied by
the 1, gives a result
exactly
equal to the remainder 901. The
figure 1
is therefore the third
and final digit
in the answer, The square root of 2,034.01 is therefore 45.1 Your completed
computation appears as:
