Question

How do we Rationalise the denominator?

Answer 1

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.


Step 2: Make sure all radicals are simplified.

Step 3: Simplify the fraction if needed.





 Example 1:   Rationalize the denominator .


 

Step 1: Multiply numerator and denominator by a radical that will get rid of the radical in the denominator.


 

Since we have a square root in the denominator, then we need to multiply by the square root of an expression that will give us a perfect square under the radical in the denominator.

Square roots are nice to work with in this type of problem because if the radicand is not a perfect square to begin with, we just have to multiply it by itself and then we have a perfect square.

So in this case we can accomplish this by multiplying top and bottom by the square root of 6:


 




*Mult. num. and den. by sq. root of 6 
  
 

*Den. now has a perfect square under sq. root 
 


 

Step 2: Make sure all radicals are simplified

AND

Step 3: Simplify the fraction if needed.


  




  
 

*Sq. root of 36 is 6 
  
 

*Divide out the common factor of 2 
 


 

Be careful when you reduce a fraction like this.  It is real tempting to cancel the 3 which is on the outside of the radical with the 6 which is inside the radical on the last fraction.  You cannot do that unless they are both inside the same radical or both outside the radical like the 4 in the numerator and the 6 in the denominator were in the second to the last fraction.