Question

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

Answer 1

`(4√(6)-√(15))/(27)`

Explanation:

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

`\mathrm{Cancel\:the\:common\:factor:}\:2\\\\=(4√(6)-√(15))/(27)`