How do you rationalize the denominator $8/(3+sqrt5)$ ?

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Answer 1 · 2015-05-30T23:50:33

Multiply numerator (top) and denominator (bottom) by the conjugate
$3-sqrt(5)$ ...

$8/(3+sqrt(5)) = (8(3-sqrt(5)))/((3+sqrt(5))(3-sqrt(5)))$

$=(24-8sqrt(5))/(3^2-sqrt(5)^2)$

$=(24-8sqrt(5))/4$

$=6-2sqrt(5)$

How do you rationalize the denominator 8/(3+sqrt5)8/(3+sqrt5)?