Laws of Surds

 

 

 Rationalizing the denominator

 

The idea of rationalizing the denominator is to simplify a fraction such that there are no surds in the denominator. This is done by multiplying the numerator and denominator by the conjugate surd of the denominator. Rationalizing the denominator is an important idea as it simplifies algebraic manipulation, for example, in combining two fractions involving surds.

 

  Simplify the following fractions:

 

 

 

 

       

                   =      this does not change the magnitude of the expression as it
                                                      is essentially multiplying by 1

                   =

                   =

                   =

 

 

 

 

      

                   =

                   =

                   =

 

 

 

 

       

                   =

                   =