Radicals. 4 1 



17. Examples. Give the value of each of the following ex- 

 pressions in as simple a form as possible : 



/, IQv/i-fv/ looo. 



P '2v/"3 3v/^ 



^- 3^ 2-2^ 3' 



J. 2 >/48-f 3^ 147-5^75- 



/. v/98-f 'v/72H-\/ 242. 



5. v^7"5^*+ n/27^s_^ v/48«^^^ 



^. |v4o^=— 3V625Jt-^-f io>^5000.r'". 



^' 7 J '\ I Sx^ yS ^ 5-^'S 8 ij/ * 



JP 2.n/1-|_7_-^_2_0:_J_v/4 



"^ • ■) 5^8^147 2 ^ ^• 



P- 



J~— V2"^ + 'V.r="^^ 



fx 

 /o. Prove 



\ a'x+x'—2ax ' \ a'x'-\-x^-^2ax' _ j «N--^ | / 



18. Multiplication and Division of Radicals. The pro- 

 duct of several radicals of the same index may be expressed as a 

 single radical by means of Art. 5. Thus 



'v^2X V/3X v/5 = n/2 X3X5=v^30 ; 

 ^r^r'X ^ mx X ^ r^ = -^x ^ r*m^= rx^rnf ; 

 V^xV(^Xv/<r. . . ='^a d c . . . 

 The result should always be reduced to its simplest form. If 

 there are coefficients they should be multiplied together for a new 

 coefficient, for 



a\''^x b'y/y c"'>/ z=-abc'\^ x Vj/ '^^ z=abc^ xyz. 

 The quotient of one radical by another of the same index may 

 be expressed as a single radical by means of Art. 6. Thus 



^5^"^^=v/rJr^^'' 



V'b sjb b 



Va-^Vb==^-=" yt^'^Vab"- 



The result should always be expressed in its simplest form. 



If we wish 'to multiply or divide radicals of different indices we 



must first reduce them to a common index. This can be done by 

 A— 5 



