Question

(sqrt(6))/(8+\sqrt(10))

Answer 1

Answer:

$\frac{4\sqrt{6}-\sqrt{15}}{27}$

Step-by-step explanation:

$\frac{\sqrt{6} }{8+\sqrt{10} } \\\\\mathrm{Multiply\:by\:the\:conjugate}\:\frac{8-\sqrt{10}}{8-\sqrt{10}}\\=\frac{\sqrt{6}\left(8-\sqrt{10}\right)}{\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)}\\\\\sqrt{6}\left(8-\sqrt{10}\right)=8\sqrt{6}-2\sqrt{15}\\\left(8+\sqrt{10}\right)\left(8-\sqrt{10}\right)=54\\\\=\frac{8\sqrt{6}-2\sqrt{15}}{54}\\\\\mathrm{Factor}\:8\sqrt{6}-2\sqrt{15}:\quad 2\left(4\sqrt{6}-\sqrt{15}\right)\\\\=\frac{2\left(4\sqrt{6}-\sqrt{15}\right)}{54}$

$\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=\frac{4\sqrt{6}-\sqrt{15}}{27}$