How do you simplify #1/(3+sqrt5) #?

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Answer 1 · 2018-04-07T13:29:05

#(3-sqrt5)/4#

Rationalize the denominator (radicals cannot be in the denominator) by multiplying the numerator and denominator by #3-sqrt5#

#1/(3+sqrt5)#

#(1*3-sqrt5)/((3+sqrt5)(3-sqrt5))#

#(3+sqrt5)(3-sqrt5)=9-3sqrt5+3sqrt5-sqrt25#

#9-3sqrt5+3sqrt5-sqrt25=9-5=4#

#(3-sqrt5)/4#

Answer 2 · 2018-04-07T13:30:29

#(3-sqrt(5))/4#

You can rationalise the denominator by multiplying by it’s conjugate.

#1/(3+sqrt(5))times(3-sqrt(5))/(3-sqrt(5))#

#=(3-sqrt(5))/(9-5)#

#=(3-sqrt(5))/4#