Question

4. Rationalize the denominator and simplify. 5+√5/8-√5

Answer 1

$\frac{5+ \sqrt{5} }{8- \sqrt{5} } = \frac{5+ \sqrt{5} }{8- \sqrt{5} } * \frac{8+\sqrt{5}}{8+\sqrt{5}} = \frac{(5+\sqrt{5})*(8+\sqrt{5})}{(8-\sqrt{5})*(8+\sqrt{5})} = \frac{40+5 \sqrt{5}+8 \sqrt{5}+( \sqrt{5})^2 }{64+8\sqrt{5}-8\sqrt{5}-( \sqrt{5})^2} =$
$\frac{40+13 \sqrt{5}+5 }{64-5} = \boxed{\frac{45+13 \sqrt{5} }{59} }$