Question

What is the following quotient -2 srt8 4+sqrt 12

Answer 1

`(-2\sqrt8)/(4+√(12))=(-2√(4\cdot2))/(4+√(4\cdot3))=(-2\cdot\sqrt4\cdot\sqrt2)/(4+\sqrt4\cdot\sqrt3)=(-2\cdot2\sqrt3)/(4+2\sqrt3)=(-4\sqrt2)/(2(2+\sqrt3))=-(2\sqrt2)/(2+\sqrt3)\\\\\text{Use}\ (a+b)(a-b)=a^2-b^2\\\\=(-2\sqrt2)/(2+\sqrt3)\cdot(2-\sqrt3)/(2-\sqrt3)=(-2\sqrt2(2-\sqrt3))/(2^2-(\sqrt3)^2)\\\\\text{Use distributive property and}\ √(a)\cdot√(b)=√(ab)\\\\=(-4\sqrt2+2\sqrt6)/(4-3)=(2\sqrt6-4\sqrt2)/(1)=2\sqrt6-4\sqrt2`