...ARITHMETICAL CALCULATIONS BY LOGARITHMS. § 27. Multiplication, Try Logarithms. Since the logarithm of the product of two or more factors is equal to the sum of their logarithms, we deduce, for multiplication by logarithms, this • RULE. / Add the logarithms...

...sometimes called Surds. Such expressions may often be simplified, by employing the principle that, the square root of the product of two or more factors is equal to the product of the square roo'- of these factors ; or, in algebraic language, 1/abcd . . . = i/a . -\/b . •)/ c. -^ d . . ....

...Surds may frequently be simplified by the application of the following principle : the square root vf the product of two or more factors is equal to the product of the square roots of those factors : Or, in algebraic language, for each member of this equation, squared, will give the...

...l * х-}- 1 ж" — l MULTIPLICATION OF RADICALS. 253. It has already been shown (337) that the nth root of the product of two or more factors is equal to the product of t lie nth roots of those factors. And since the converse of this proposition is true, we shall have...

...\fa Vi Ve Vk ; or, with fractional exponents, .L -L -L -L -l (auc &)" =a"u"c" ¿". That is, The nth root of the product of two or more factors is equal to the product of the nth roots of the factors. 328. There are certain properties of roots which depend upon the law of signs...

...must be divided by the index of the root. For, since the rcth power of am is a"'" (Art. 201), 212. 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, it has been shown, in raising a quantity composed of factors...

...degree 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=1/aXi/6, and l/36=v/9><1/4; for v/36=±6, and y/9X V 4=3X2=6. Any radical...

...degree 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, ,/o6=i/aXv/*i and ,/36=,/9X,/4; for ^^=±6, and v/9Xi/4~=3X2=6. f Any radical...

...quantities, without altering their value. Reduction of radicals of the second degree is founded on the following principle : <*.: The square root of the product of two or more factors is equal If the product of the square roots of those factors : That is, *Jab=tJaX'Jb ; which is thus proved...

...Eadical 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...