MATHEMATICS 15 



being one of hundreds, we have no longer anything to do 

 with sets of ten only, and still less with mere units. 

 Having now these three products of the addition of 2063 

 to itself 5 times, 40 times, 300 times, we have but to 

 place them one under the other and add them up 

 thus : 



7H735 



And thus we know that the result of the addition is 

 equivalent to the adding 2063 to itself 345 times. 



When a number is multiplied (added to itself) its own 

 number of times, as, e.g., 5, five times, or 9, nine times, or 

 1000, a thousand times, the product is called the square 

 of each such number. The number which, by so multi- 

 plying itself, makes that product, is called the square 

 root of that same product whatever it may be. 



When the square of a number is again multiplied by 

 that number, the product is called a cube, and the original 

 number is the cube root of such product. 



The square, or the cube, of a number may be represented 

 by a small figure, which is called an index, placed on one 

 side above the number squared or cubed. Thus the 

 indices 2 and 3 thus placed with respect to 4, will be 4 2 

 and 4 3 ; and these two symbols respectively indicate 4 

 squared and 4 cubed which are, of course, 16 and 64. 

 The symbols J and J/ indicate respectively the square and 

 cube roots of any numbers, and thus ^16 is 4 and the ^64 

 is also 4. 



The number of times any quantity is thus multiplied 

 by itself is called its " power." Thus 2 7 , or 2 raised to 



