5>aos^ 



48 * Algebra. 



= l6^ + (3'X5)^J f6''^-6^X3X5^+6X3''X5'-3'X5*J 

 = 6^-3^X5=891. 



J. Rationalize N^ 2 + 2^ 9. 



28. Rationalization of thk Denominators of Frac- 

 TiONS. The most common application of rationalizing factors is 

 in the rationalization of the denominators of irrational fractions. 

 Considerable labor is saved in computing the value of a numeri- 

 cal irrational fraction if we first rationalize the denominator. 



Thus, to compute the value of -._ y^ correct to five decimal 



V 7 — V 2 



places, three square roots must be taken and one of them must be 

 divided by the difference of the other two. Now, it will be obvious 

 on reflection that these square roots must be taken to nearly ten 

 places of decimals if we are to be absolutely certain that five deci- 

 mal places of the quotient are correct. It will be easily seen how 

 much more readily the value can be found after the denominator 

 has been rationalized. Multiplying both numerator and denomi- 

 nator by the rationalizing factor for the denominator, w^ have 



>^5 ^ -y ^W -j-^r^ 2) ^ ^3 5 +^ 10 

 v^7 — x/^ (>/y_v/2)(s/7 + v/2)~ 5 



Now but t7£fo square roots need be taken, and these to no more 

 than five decimal places, since the exact value of the denominator 

 is known. 



29. Examples. 



. v/6 



1. Rationalize the denominator of — := -. 



2. Rationalize the denominator of ^^^=-^ — j=. 



•^2 + ^i 



f 2 ] ^ „ 1 



J. Prove I ^\ =(2 — ^^2)2. 



l2 + V^2J 



/. Given x^ 3= 1.7320508, find the value of -=i. 



