Question

Simplify 2 root 6/ root 2 + root 3 + 6 root 2/ root 2 + root 3- 8 root 3 / root 6 +root 2

Answer 1

see the attachment for your answer....

hope it help

Answer 2

Answer:The required simplified form of the given expression is,

$-4\sqrt{3}+8\sqrt{6}-12$

Step-by-step explanation:

Here, the given expression is,

$\frac{2\sqrt{6}}{\sqrt{2}+\sqrt{3}}+\frac{6\sqrt{2}}{\sqrt{2}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}$

$=\frac{2\sqrt{6}+6\sqrt{2}}{\sqrt{2}+\sqrt{3}}-\frac{8\sqrt{3}}{\sqrt{6}+\sqrt{2}}$

By rationalization,

$=\frac{(2\sqrt{6}+6\sqrt{2})(\sqrt{2}-\sqrt{3})}{2-3}-\frac{8\sqrt{3}(\sqrt{6}-\sqrt{2})}{6-2}$

$=\frac{(2\sqrt{6}+6\sqrt{2})(\sqrt{2}-\sqrt{3})}{-1}-\frac{8\sqrt{3}(\sqrt{6}-\sqrt{2})}{4}$

$=\frac{2\sqrt{12}-2\sqrt{18}+12-6\sqrt{6}}{-1}-\frac{8\sqrt{18}+8\sqrt{6}}{4}$

$=\frac{-8\sqrt{12}+8\sqrt{18}-48+24\sqrt{6}-8\sqrt{18}+8\sqrt{6}}{4}$

$=\frac{-8\sqrt{12}+32\sqrt{6}-48}{4}$

$=-2\sqrt{12}+8\sqrt{6}-12$

$=-4\sqrt{3}+8\sqrt{6}-12$