How do you rationalize the denominator and simplify 1/ (sqrt 3 - sqrt 5)1√3−√5?
1 Answer
May 13, 2016
Explanation:
What we have to do here is to multiply the numerator and denominator by the
color(blue)" conjugate"" of the denominator" conjugate of the denominator The conjugate here is
sqrt3+sqrt5√3+√5 Note that the radicals remain unchanged ,while the 'sign' changes.
If
sqrt3-sqrt5" then conjugate" =sqrt3+sqrt5√3−√5 then conjugate=√3+√5
rArr1/(sqrt3-sqrt5)=(1(sqrt3+sqrt5))/((sqrt3-sqrt5)(sqrt3+sqrt5))⇒1√3−√5=1(√3+√5)(√3−√5)(√3+√5) Consider the denominator.
(sqrt3-sqrt5)(sqrt3+sqrt5)" and expand using FOIL"(√3−√5)(√3+√5) and expand using FOIL
=(sqrt3)^2+cancel(sqrt5 .sqrt3)-cancel(sqrt5 .sqrt3)-(sqrt5)^2
=3-5=-2" which is rational"
rArr1/(sqrt3-sqrt5)=(sqrt3+sqrt5)/(-2)=-1/2(sqrt3+sqrt5)
