SURDS. 321 



3 5 -3 



6. Required the sum of y/40 and v/13^. Ans. S\/S* 



3 3 3 



7. Required the sum of y/^ and v^jV* ^^^' i\/^' 



PROBLEM V. 



To subtract, or find the difference of, surd quantities. 



RULE. 



Prepare tKe quantities as for addition, and tKe differ- 

 ence of the rational parts, annexed to the common surd, 

 will give the difference of the surds required. 



But if the quantities have no common surd, they can 

 only be subtracted by means of the sign — . 



EXAMPLES. 



1, Required to End the difference of v^448 and y/xI2. 

 First, v/443=z^64X7 = 8v/7 5 



And v^ii2=:-v/i6X7=4\/7 5 



Then 8^/7 — 4^/7 — 4 v/T ^he difference required. 



Z X 



2. Required to find the difference of 192^ and 24^. 



First, 192^ z=64X3l' = 4X3 



And 24^= 8X3P = 2X3' 5 



I T I 



Then, 4X3^ — 2X3^=^X3^ ^^ difference re- 

 quired. , 

 I 3. Required the difference of 2^/50 and v^i8. 



Ans. 7v/2. 



4. Required the difference of 3 20 ^ and 40 ^ . 



X 



Ans. 2X5"^. 

 R R 5. Required 



