How do you rationalize the denominator $(1+sqrt2)/(3+sqrt5)$ ?

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Answer 1 · 2015-05-28T22:15:43

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

$(1+sqrt(2))/(3+sqrt(5))$

$= (1+sqrt(2))/(3+sqrt(5))*(3-sqrt(5))/(3-sqrt(5))$

$= ((1+sqrt(2))(3-sqrt(5)))/((3+sqrt(5))(3-sqrt(5)))$

$= ((1+sqrt(2))(3-sqrt(5)))/(3^2-sqrt(5)^2)$

$= ((1+sqrt(2))(3-sqrt(5)))/(9-5)$

$= ((1+sqrt(2))(3-sqrt(5)))/4$

How do you rationalize the denominator (1+sqrt2)/(3+sqrt5)(1+sqrt2)/(3+sqrt5)?