 | Bourdon (M., Louis Pierre Marie) - Algebra - 1831 - 326 pages
...second degree. 84. These expressions may be often simplified by the use of the following principle. The square root of the product of two or more factors...equal to the product of the square roots of these factor t, or, in algebraical language, v/abcd • • • • = v/a • v/^ • \'c • V^ • •... | |
 | Charles Davies - Algebra - 1835 - 378 pages
...called radical quantities, or irrational quantities, or simply radicals of the second degree. 125. These expressions may sometimes be simplified, upon the principle that, the square root of tlie product of two or more factors is equal to the product of the square roots of these factors ;... | |
 | A. Turnbull - Arithmetic - 1836 - 368 pages
...~ represent a fraction in its least terms. Then . a *.'aa \/ab 820. The root of any number which is the product of two or more factors, is equal to the product of the roots of these separate factors. Thus \/ab — \/a X ,,/b. If o = 10 and b — 9, then */ Hi X » =... | |
 | Bourdon (M., Louis Pierre Marie) - Algebra - 1839 - 368 pages
...called radical quantities, or irrational quantities, or simply radicals of the second degree. 125. These expressions may sometimes be simplified, upon...square root of the product of two or more factors » equal to the product of the square roots of these factors ; or, in algebraic language, Vabcd . .... | |
 | Charles Davies - Algebra - 1840 - 264 pages
...simply radicals of the second degree. They are also, sometimes called Surds. These expressions may often be simplified, upon the principle that, the square root of the product of two or more factors w equal to the product of the square roots of these factors ; or, in algebraic language, Jyabcd . .... | |
 | Davis Wasgatt Clark - 1844 - 394 pages
...rule for the involution of monomials, let the following proposition be demonstrated, viz. : The power of the product of two or more factors is equal to the product of their powers. Let («6)2 represent the second power of the product of two factors, And a262 the product... | |
 | Charles Davies - Algebra - 1845 - 382 pages
...it follows, that the quantities themselves are equal : hence, -\Jabcd = ya . yb . yc . yd; that is, The square root of the product of two or more factors is equal to the product of the square roots of those factors. This being proved, we can write I In like manner, X 5bd = 3abc -V/864a265cil = v/144a264cio... | |
 | Davis Wasgatt Clark - Algebra - 1846 - 374 pages
...rule for the involution of monomials, let the following proposition be demonstrated, viz.: The power of the product of two or more factors is equal to the product of their powers. Let (ab) 2 represent the second power of the product of two factors, And aV the product... | |
 | Elias Loomis - Algebra - 1846 - 376 pages
...+ x' is the index of that power of the base a which is equal to NN' j that is to say, The logarithm of the product of two or more factors is equal to the sum of the logarithms of tho2e factors. Hence \ve see that if it is required to multiply two or more... | |
 | Charles William Hackley - Algebra - 1846 - 542 pages
...together, NN'=a'a" =a"+" .-. by definition, r+x' is the logarithm of NN' ; that is to say, The logarithm of the product of two or more factors is equal to the sum of the logarithms of those factors. II. Divide equation (1) by (2). N_o« N'=o" =a'-". .•. by... | |
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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. 
