SQUARE MEASURE 



5514 



SQUARE ROOT 



V/T44=? The answer, or 12, is called the square 

 root of 144. The problem is expressed thus: 



Area of square = 144 sq. ft. 



1 side in ft.= y 7 144 = 12 



The line upon which a square is built is 

 called the root of the square. 



Related Subjects. In connection with this 

 discussion of the square, the reader is referred 

 to the following articles in these volumes: 

 Mensuration Square Measure 



Quadrilateral Square Root 



Rectangle 



SQUARE MEASURE, the system used in 

 the measurement of surfaces. The name is 

 taken from that of the square, or the unit em- 

 ployed in finding the area of a surface. The 

 table of common square measure is given in 

 these volumes on page 1763, under the title 

 DENOMINATE NUMBERS. For practical applica- 

 tions of the principles of square measure, see 

 MENSURATION. 



SQUARE ROOT. On a line 4 inches long 

 build a square. The area of the square is 16 

 square inches. On a line 9 feet long build a 

 square. The area of the square is 81 square 

 feet. On a line 8 units long build a square. 

 The area is -64 square units. 



The drawing of many squares on cross-sec- 

 tion paper, as suggested above, shows the 

 meaning of a square, and makes clear the rela- 

 tion of the area of a square to one of its sides; 

 namely, the number of square units in the area 

 is equal to the number of units 'in one side 

 multiplied by itself. This product is called 

 "the square" of the number. "The square" is 

 used to designate the product obtained by 

 multiplying a number by itself, whether or not 

 that product is thought of geometrically as a 

 squared The square of a number is indicated 

 by a little figure called an exponent; thus 

 42-16; 92=8!. 



The above are read: 4 squared 16; 9 

 squared=81 ; or the square of 4 = 16; the square 

 of 9=81. 



The area of a square is 144 square feet. 

 What is one side? 12 feet. 



The area of a square is 169 square miles. 

 What is one side? 13 miles. 



Note the relation between areas and sides 

 below. 



Areas Side 



400 sq. ft. 20 ft. 



36 sq. in. 6 in. 



49 sq. yd. 7 yd. 



121 sq. rd. 11 rd. 



gives a certain square, is called "finding the 

 square root of the number," that is, finding the 

 line or number out of which the square grows. 

 And, as is usual in mathematics, there is a sign 

 used to indicate what is sought; thus V25 

 stands for the number which multiplied by it- 

 self makes 25. The sign is called the radical 

 sign root sign. 



Find the values of the following: 



52 



I 2 



142 



302 



V6400 



x/144 



V14400 



402 



VT69" 



Squaring a Number Consisting of 10's and 

 Units. Square 46. 



46 = 4 tens + 6 units 

 462= 

 40 +6 

 40 +6 



40 



402+2x(40X6)+62 

 1600 +480 +36 = 2116 



392= (30 + 9) 2 = 302 + 2 x (30X9) +92 

 39 

 39^ 



81 =9X9 



270 =9X30 



270 =30X9 



900 =30X30 



1521 =39X39 



The square contains the square of the tens, 

 twice the product of the tens by the units, and 



2. 



406 



86 



the square of the units. This may be put into 

 Finding the line upon which a square is built, a more concise form, thus : 



or finding what number multiplied by itself 



number 2 =tens 2 +2XtensXunits+units 2 



