How do you simplify (2 -sqrt 5) /(3 +sqrt5)?

2 Answers
sankarankalyanam
Jun 20, 2018

color(chocolate)(=> 11/4 - (5sqrt5)/4

Explanation:

(2 - sqrt5) / (3 + sqrt5)

=> ((2 - sqrt5) * (3 - sqrt5)) / ((3 + sqrt5) (3 - sqrt5))

=> (6 - 2 sqrt5 -3sqrt5 + 5 ) / (9 - 5)

=> (11 - 5sqrt5) / 4

color(chocolate)(=> 11/4 - (5sqrt5)/4

Jim G.
Jun 20, 2018

11/4-(5sqrt5)/4

Explanation:

"multiply the numerator/denominator by the "color(blue)"conjugate"
"of the denominator"

"the conjugate of "3+sqrt5" is "3color(red)(-)sqrt5

=((2-sqrt5)(3-sqrt5))/((3+sqrt5)(3-sqrt5))

"expand factors on numerator/denominator"

=(6-5sqrt5+5)/(9-5)

=(11-5sqrt5)/4=11/4-(5sqrt5)/4

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