Rationalization of Surd or Radical -- Part 3

                                            Surd Part III

So far, you read about introduction of Radical, type of surds, pure and mix.  Now, we shall know about other forms of radical or surd with solved examples as well as Rationalization of surds: I hope you will find it easy and interesting.

Now, we learn how to express each of surds:- 



1.  a √a + b
a√a + b = a. (a + b)^1/2  
              =(a²)^1/2 . (a + b)^1/2
              =[a² . (a + b)^1/2
              =√a³ + a²b


(ii) a³√b²
                =a³√ b² 
                = a. (b²)^1/3
                =(a³)^1/3 . (b²)^1/3
                = (a³b²)^1/3
               =3√a³ + ab2


Rationalization of Surds:-


When the product of two surds is a rational number, then each surd is called a rationalizing factor (RF) of the other.

(i) ³√9 X ³√3 = ³√9x3 =³√3³ =3 which is a rational number
Hence, ³√9 + ³√3  are rationalizing factors of each other.



Rationalization  of Surd to a rational number by multiplying it with a suitable rationalizing factor is called the rationalization of the surd.




Mononial surds and their Rationalization: A surd consisting of only one term is known as a monomial surd. √2,  √7, 3√6 etc. are monomial surds.




Rationalizing Factor of a monomial surd: one of the rationalizing factors of a^1/n is a^{(1 – 1/n)}