\fdO'^ - Old Forge Coal Mines

72 ARITHMETIC.
in the root. Write in the root, as shown, and also add it
to the trial divisor, 600, and annex a cipher, thereby making
the next trial divisor 6,000. Bring down the next period, 99.
The trial divisor 6,000 is contained in 000099, times, so we
place as the next figure in the root, as shown, and also add
it to the trial divisor 6,000, and annex a cipher, thereby mak-
ing the next trial divisor 60,000. Bring down the next period,
40, and annex it to the dividend already obtained to form
the new dividend, 00009940, and divide it by the trial divisor
60,000. 60,000 is contained in 00009940, times, so we place
another cipher in the root, as shown, and also add it to the
trial divisor 60,000, and annex one cipher, thereby making
the next trial divisor 600,000. Bring down the next period,
09, and annex it to the dividend already obtained to form
the new dividend, 0000994009, and divide it by the trial divisor
600,000. 600,000 is contained in 0000994009 once,
we place 1 as the next figure in the root, and also add it
so
to
the trial divisor 600,000, thereby making the complete divisor
600,001. Multiply the complete divisor, 600,001, by 1, the
sixth figure in the root, and subtract the result obtained
from the dividend. The remainder is 394,008, to which we
annex the next period, 00, to form the next new dividend, or
39,400,800. Add the sixth figure of the root, or 1, to the
divisor 600,001, and annex a cipher, thus obtaining 6,000,020
as the next trial divisor. Dividing 39,400,800 by 6,000,020,
we find 6 to be the next figure of the root. Adding this last
figure, 6, to the trial divisor, we obtain 6,000,026 for our
next complete divisor, which, multiplied by the last figure of
the root, or 6, gives 36,000,156, which write under 39,400,800
and subtract. Since there is a remainder, it is clearly evident
that the given power ^is not a perfect square, so we
place -\- after the root. Since the next figure is 5, the
answer is — .
3,000.017
In this problem there are seven periods—four in the whole
number and three in the decimal—
hence, there will be seven
figures in the root, /our figures constituting the whole
number, and three figures the decimal of the root.
4/9,000,099.4009 = 3,000.017 -.
Hence,