\fdO'^ - Old Forge Coal Mines

ARITHMETIC. 76
Explanation.— (1) When extracting the cube root we
divide the power into periods of three figures each. Always
begin at the decimal point, and proceed to the left in point-
ing off the whole number, and to the right in pointing off
the decimal. In this power >^. 32768, a cipher must be
annexed to 68 to complete the second decimal period.
Cipher periods may now be annexed until the root has as
many figures as desired.
(2) We find by trial that the largest number whose cube
is contained in the first period, 327, is 6. Write 6 as the first
figure of the root, also at the extreme left at the head of
column (1). Multiply the 6 in column (1) by the first figure
of the root, 6, and write the product 36 at the head of
column (2). Multiply the number in column (2) by the
first figure of the root, 6, and write the product 216 under
the figures in the first period. Subtract and bring down
the next period 680; annex it to the remainder 111, thereby
obtaining 111,680 for a new dividend. Add the first figure
of the root, 6, to the number in column (1), obtaining
12, which we call the first correction ; multiply the first
correction 12 by the first figure of the root, and we obtain
72 as the product, which, added to 36 of column (2), gives
108. Annexing two ciphers to 108, we have 10,800 for the
trial divisor. Dividing the dividend by the trial divisor, we
see that it is contained about 8 times,
so we write 8 as the
second figure of the root. Add the first figure of the root
to the first correction, and we obtain 18 as the second cor-
rection. To this annex one cipher, and add the second figure
of the root, and we obtain 188. This, multiplied by the second
figure of the root, 8, equals 1,504, which, added to the
trial divisor •
10,800, forms the complete divisor 12,304.
Multiplying the complete divisor 12,304 by 8, the second
figure of the root, the result is 98,432. Write 98,432 under
the dividend 111,680; subtract, and there is a remainder
of 13,248. To this remainder annex the next period 000,
thereby obtaining 13,248,000 for the next new dividend.
(3) Adding the second figure of the root, 8, to the number
in column (1), 188, we have 196 for the first new