How do you simplify #3/ (6- sqrt 5)#?

Question

2832 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-03-13T10:20:49

#3/(6-sqrt 5) = 3/31 (6+sqrt 5) #

By rationalizing the denominator:

#3/(6-sqrt 5) xx (6+sqrt 5)/(6+sqrt 5)#

#= (3 xx (6+sqrt 5)) / (6^2 - (sqrt5)^2)#

#= (3xx(6+sqrt 5)) / (36-5)#

#= 3/31 (6+sqrt 5) #

Answer 2 · 2018-03-13T10:24:01

Multiply the numerator and denominator by the conjugate of the denominator and simplify

#3/(6-sqrt(5))#
#color(white)("XXX")=3/(6-sqrt(5)) * (6+sqrt(5))/(6+sqrt(5))#

#color(white)("XXX")=(3(6+sqrt(5)))/(6^2-(sqrt(5))^2)#

#color(white)("XXX")=(18+3sqrt(5))/(36-5)#

#color(white)("XXX")=(18+3sqrt(5))/31#