feVOLUTION. J 13 



EXAMPLES. 



t. The square root of ^x^ zz-^x^zr^X, 



2. The cube root of Sx^ =z 2X ^ = 2x. 



± A 



3. The square root of 3^ ^ a; ^ = « - a; - ^3 = ax ^ y/i'. 



i £ 

 4* The cube root of — 125^^^?*^= — S^^x^'zz — 5^A?*. 



5. The biquadrate root of i6a^;v^ = 2«'^A^'^=2^iV*. 



CASE II. 

 ^ofind the square root of a cotnpound quantity. 



liULE. 



1. Range the quantities according to the dimensions of 

 some letter, and set the root qf the first term in the quo- 

 tients 



2. Subtract the square of the root, thus found, from 

 the first term, and bring down the tWo next terms to the 

 remainder for a dividend. 



3. Divide the dividend by double the root, and set the 

 result in the quotient. 



4. Multiply 



And an odd root of any quantity will have the same sign as 

 the quantity itself : thus, the cube root of -j-^^ is -f-,<? 5 and the 

 cube root of — a^ is — ^ ; for +« X -{-<« X 4-«= +^ ^ ; and — a 

 X — a% — a—a'^. 



Any even root of a negative quantity Is impossible ; for neither 

 ^a%-\-ai nor —aY, — a, can produce — a"^ , 



Any root of a product is equal to the product of the like roots 

 of all the factors. And any root of a fraction is equal to the 

 like^ root of the numerator, divided by the like root of the de- 

 nominator. 



