How do you rationalize the denominator and simplify 3/(6-sqrt5)36−√5?

1 Answer
Shwetank Mauria
Apr 4, 2016

18/31+3/31sqrt51831+331√5

Explanation:

WE can rationalize the denominator in 3/(6-sqrt5)36−√5 by multiplying numerator and denominator by conjugate of the denominator. The conjugate of (6-sqrt5)(6−√5) is (6+sqrt5)(6+√5).

Hence 3/(6-sqrt5)=(3*(6+sqrt5))/((6-sqrt5)(6+sqrt5))36−√5=3⋅(6+√5)(6−√5)(6+√5)

= (18+3sqrt5)/(36-5)18+3√536−5 or

= 18/31+3/31sqrt51831+331√5

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