This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 Excerpt: ...He has only to notice whether the cube, whose root Note. The common method for proving the cube root is to cube the root, and add the remainder, if any: if that agrees with the number to be extracted, the work is right: but the readiest way to prove the cube root is this, subtract the excess nines in the remainder from ...
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This historic book may have numerous typos and missing text. Purchasers can download a free scanned copy of the original book (without typos) from the publisher. Not indexed. Not illustrated. 1837 Excerpt: ...He has only to notice whether the cube, whose root Note. The common method for proving the cube root is to cube the root, and add the remainder, if any: if that agrees with the number to be extracted, the work is right: but the readiest way to prove the cube root is this, subtract the excess nines in the remainder from the number to be extracted, reject the excess of nines in that number, and if it agrees with the cube of the excess of nines in the root, the operation will be right, for example, in the above remainder the excess of the nines is 0; in the number to be extracted there is an excess of 1. The excess of nines in the root is 4, the cube of which is 64; and the excess of nines is 1; and therefore the operation is presumed to be right; or thus, 4 X 4=16, the sum of whose digits is 7-7 X 4=28, the sum of whose digits is 10, being an excess of the nines by 1 as before. To persons unaccustomed to the rejection of the nines in arithmetical operations, it may appear tedious at first; but a little practice will make this plain and easy; it is, however, advisable to prove the operations in the cube root in this manner, on obtaining each remainder, and before the next figure is placed in the root. What is the cube root of 7-684367? 7-684367 Here the nearest cube to the first point is 1; but as 7 is so near to 8, the cube root of which is 2, look to the table from 200, and proceed back, and opposite the cube of 197 you will find 7645373; but as there can be but one whole number in the root, consequently the 197 will, in the root, become 1-97, the cube of which instead of 7645373 is 7-645373. Hence the operation is as follows. 7-684367 (1-973 7-645373 197 X 197 X 300=11642700)38994000 34928100 159570 27 3906303 remainder. NOTE CONTINVED. is required, consist...
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