Question

Plz help. I need this by tomorrow or I’ll get detention.

Answer 1

`(6+ √(27))/(4-\sqrt3) \\\\\\=(\left(6+√(27)\right)\left(4+\sqrt 3 \right))/(\left(4-\sqrt 3\right) \left(4+\sqrt 3\right))\\\\\\=(24+6\sqrt 3+4√(27)+√(27\cdot 3))/(4^2 - \left(\sqrt 3 \right)^2)\\\\\\=(24+6\sqrt3+4√(9\cdot 3) +√(81))/(16-3)\\\\\\=(24+6\sqrt 3 +12\sqrt 3 + 9 )/(13)\\\\\\=(33+18\sqrt 3)/(13)\\\\\\\text{Hence, r = 33 and s = 18}`