How do you rationalize the denominator $(2+sqrt3)/(5-sqrt3)$ ?

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Answer 1 · 2015-04-01T19:18:54

$(2 + sqrt(3))/(5 - sqrt(3)) = ((2 + sqrt(3))xx(5 + sqrt(3)))/((5 - sqrt(3))xx(5 + sqrt(3))$

$= (10 + 5sqrt(3) + 2sqrt(3) + (sqrt(3))^2)/(25 - (sqrt(3))^2)$

$= (10 + 3 + 8sqrt(3))/(25 - 3)$

$= (13 + 8sqrt(3))/(22)$

How do you rationalize the denominator (2+sqrt3)/(5-sqrt3)(2+sqrt3)/(5-sqrt3)?