How do you rationalize $(6-sqrt7)/(5-sqrt7)$ ?

Question

1537 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2015-06-01T21:04:05

Multiply both numerator (top) and denominator (bottom) by the conjugate $5 + sqrt(7)$ ...

$(6-sqrt(7))/(5-sqrt(7))$

$= (6-sqrt(7))/(5-sqrt(7))*(5+sqrt(7))/(5+sqrt(7))$

$= ((6-sqrt(7))(5+sqrt(7))) / ((5-sqrt(7))(5+sqrt(7)))$

$= (30+sqrt(7)-sqrt(7)^2)/(5^2-sqrt(7)^2)$

$= (30+sqrt(7)-7)/(25-7)$

$=(23+sqrt(7))/18$

How do you rationalize (6-sqrt7)/(5-sqrt7)(6-sqrt7)/(5-sqrt7)?