 It is founded on the following principle. The square root of the product of two or more factors, is equal to the product of the square roots of those factors.  Elements of Algebra - Σελίδα 106των Bourdon (M., Louis Pierre Marie) - 1831 - 304 σελίδεςΠλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | Robert Wallace - 1870 - 164 σελίδες
...x-\-x' -\-x" -\-, &c.=log. yy'y"=log. y-(-log. y'-(-log y". F'rom which it is evident that the logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. (156.) Hence, if all the factors of a given number be supposed... | |
 | Joseph Ray - 1866 - 420 σελίδες
...radicals consists in changing the form of the quantities without altering their value. It is founded on the following principle : The square root of the product...factors is equal to the product of the square roots of those factors. That is, 1/o6=l/aXv/^! which is thus proved; Squaring both members of this equation,... | |
 | Elias Loomis - 1871 - 302 σελίδες
...98.7654; " " " 1.647817 is .444444 MULTIPLICATION BY LOGARITHMS. (11.) According to Art. 3, the logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. Hence, for multiplication by logarithms, wa have the following... | |
 | Elias Loomis - 1873 - 396 σελίδες
...Badical quantities may frequently be simplified by the application of the following principle : the nth root of the product of two or more factors is equal to the product of the nth roots of those factors ; or, in algebraic language, For each of these expressions, raised to the... | |
 | James Bates Thomson - 1878 - 322 σελίδες
...factor, with the radical sign between them. NOTES. — I. This rule is based upon the principle that the root of the product of two or more factors is equal to the product of their roots. 2. When the radicals are small, the greatest exact power they contain may be readily found... | |
 | Webster Wells - 1879 - 468 σελίδες
...since the nth power of am is «mn (Art. 228), it follows that the nth root of amn is a™. 236. Any root of the product of two or more factors is equal to the product of the same root of each of the factors. For, we have seen in Art. 228, in raising a quantity composed of... | |
 | 1888 - 492 σελίδες
...The following principle is useful in finding any required root of the product of several factors. Any root of the product of two or more factors is equal to the product of the same roots of the factors. Thus, л/9 хТ6 = л/9 x л/Ï6 = 3 x 4 = 12. \/ab — Va x Vb; and tyxyz... | |
 | George Egbert Fisher, Isaac Joachim Schwatt - 1898 - 712 σελίδες
...Substituting {/a*« for K in the last equation, we have *4 = a* = a« . 15. Ttie principal root of a product of two or more factors is equal to the product of the like principal roots of the factors, and conversely; or, stated symbolically, у (ab) = </ex tyb, and... | |
 | George Egbert Fisher - 1899 - 506 σελίδες
...the root; or, stated symbolically, = а ч = a*. Eg, 4/ae = a* = a2. (iii.) The principal root of a product of two or more factors is equal to the product of the like principal roots of the factors, and conversely; or, stated symbolically, У(аЬ) = 3/а xC/6,... | |
 | James Morford Taylor - 1900 - 504 σελίδες
...by notation — ~m+i»-t — to я Bummandf g yß = аяп. 119. Power of a product. Tlie nth power of the product of two or more factors is equal to the product of the nth powers of those factors ; and conversely. That is, (ab)" = a"b", (abc)" = a"b"c". Ex.1, (abc)8... | |
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