Elementary Treatise on Algebra (Paperback)

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. 1847 Excerpt: ...the second power from the left hand period. 3. To the right of the remainder bring down the next period to form a dividend. Double the root already found for a divisor. Seek how many times the divisor is contained in the dividend, rejecting the right hand figure. Place the quotient in the root, at the right of the figure previously found, and also at the right of the divisor. Multiply the divisor thus increased by the last figure of the root, and subtract the product from the whole dividend. 4. Bring down to the right of the remainder the next period. to form a new dividend. Double the root already found for a divisor, and proceed as before to find the third figure of the root. Repeat this process until all the periods have been brought down. Remark. If the dividend will not contain the divisor, the right hand figure of the former being rejected, place a zero in the root, also at the right of the divisor, and bring down the next period. Extract the roots of the following numbers. 1. 1369. 7. 36100. 2. 2401. 8. 1100401. 3. 361. 9. 1432809. 4. 123201. 10. 151905625. 5. 502681. 11. 901260441. 6. 11881. 12. 2530995481. Art. 88. There are comparatively but few numbers which are exact second powers; and the roots of such as are not perfect powers, cannot be obtained exactly either in whole numbers or fractions. For example, the root of 42 is between 6 and 7; but no number can be found, which, multiplied by itself, will produce exactly 42. We shall however see hereafter, that the root of any positive number may be approximated to any degree of exactness. Since the roots of numbers, which are not perfect powers, cannot be obtained exactly, either in whole or fractional numbers, they are said to be irrational, or incommensurable; that is, these roots and unity have ...