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SQUARE ROOT. 2 9
the longest time, namely, 2 l
/
2 years, while A has only had his
capital invested 2 years. The ratio is, therefore, not $2,000 to
$3,000 but $4,000 to $7,500, because $2,000 in 2 years is equal
to $4,000 in one year, and $3,000 in 2 l
/
2 years is equal to $7,500 in
one vear.
SQUARE ROOT.
When the square root is to be extracted the number is di-
vided into periods consisting of two figures, commencing from
the extreme right if the number has no decimals, or from the
decimal point towards the left for the whole numbers and
towards the right for the decimals. (If the last period of deci-
mals should have but one figure then annex a cipher, so that
this period also has two figures, but if the period to the extreme
left in the integer should happen to have only one figure it
makes no difference; leave it as it is.) Ascertain the highest
root of the first period and place it to the right of the number
as in long division. Square this root and subtract the product
of this from the first period. To the remainder annex the next
period of numbers. Take for divisor 20 times the part of the
root already found* and the quotient is the next figure in the
root, if the product of this figure and the divisor added to the
square of the figure does not exceed the dividend. To the
difference between this sum and the dividend is annexed the
next period of numbers. For divisor take again 20 times the
part of the root already found, etc. Continue in this manner
until the last period is used. If there is any remainder, and a
more exact root is required, ciphers may be annexed in pairs and
the operation continued until as many decimals in the root are
obtained as are wanted.
Example 1.
Extract the square root of 271,441.
Solution
:
V’27 |
14i41
52 = 25
[
20 X 5 = 100 ) 214
100 X 2 + 22 = 204
20 X 52 = 1040 ) 1041
1040 X 1 + I 2
1041
521
0000
Thus: \/271,441 = 521, because 521 X 521 = 271,441.
* If this divisor exceeds the dividend, write a cipher in the root; annex the next
period of numbers, calculate a new divisor, corresponding to the increased root, and
proceed as explained.
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