...radicals of the second degree. 84. These expressions may sometimes be simplified, upon the principle that the 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, v 'abed. . .= Va. -./b. Vc. Vd. . . . To demonstrate this principle,...

...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 ; or, in algebraic language, Vabcd . . . = ^«• v/i- Vc. ^/d. . . . To demonstrate this principle,...

...~ 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 » =...

...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...equal to the product of the square roots of these factors ; or, in algebraic language, * . -\fabcd . . . r^-y/a . -\/ b . -y/ c . -y/d . . . This being...

...also, sometimes called Surds. These expressions may often be simplified, upon the principle that, tJne 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, \/al>cd . . . =-y/a . -y/ b . -y/e . -y/ d . . i This being the...

...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...equal to the product of the square roots of these factors ; or, in algebraic language, •\/abcd . . . — -\/a . V 'b . -y/c . -v/d . . . This being...

...of the second degree. 125. These expressions may sometimes be simplified, upon the principle that, the 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, V'abed . . . = i/a. i/b. -^/c. i/d. . . . To demonstrate this principle,...

...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...

...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...

...can frequently be simplified by the application of the following principle : The square root of ike product of two or more factors is equal to the product of the square roots of these factors. Or, in algebraic language, Vabcd ..... = -/ax V&X VcX V~d- ---- • In order to demonstrate...