Rationalize the denominator

Question

Rationalize the denominator and simplify if necessary. keep as a simple fraction

sqrt49r+3/6-8sqrtr

Answer 1

√(49r + 3) / (6 - 8√r)

 

 

Multiply the numerator and denominator by the conjugate of the denominator.  Conjugate of denominator is (6+8√r).

 

 

√(49r + 3) * (6 + 8√r)

____________________   =

   (6 - 8√r) * (6 + 8√r) 

 

 

 

(6 + 8√r)(√(49r + 3))

_________________     =

      36 - 64r

 

 

 

(6 + 8√r)(√(49r + 3))

__________________

   4(9 - 16r)