Question

Simplify ...........

Answer 1

https://youtu.be/T9BmrHVPRJ0

Answer 2

Simplify:

Step-by-step explanation:

$\ Given \ value: \\\\\frac{3+\sqrt{6}}{17\sqrt{3}-2\sqrt{32}+3\sqrt{18}-4\sqrt{48}}\\\\\\\ Solution: \\\\\rightarrow \frac{3+\sqrt{6}}{17\sqrt{3}-2\sqrt{32}+3\sqrt{18}-4\sqrt{48}}\\\\\rightarrow \frac{3+\sqrt{6}}{17\sqrt{3}-2\cdot4\sqrt{2}+3\cdot3\sqrt{2}-4\cdot4\sqrt{3}}\\\\\rightarrow \frac{3+\sqrt{6}}{17\sqrt{3}-8\sqrt{2}+9\sqrt{2}-16\sqrt{3}}\\\\\rightarrow \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}$

$\rightarrow \frac{3+\sqrt{6}}{\sqrt{3}+\sqrt{2}}\times \frac{{\sqrt{3}-\sqrt{2}}}{{\sqrt{3}-\sqrt{2}}}\\\\\rightarrow \frac{(3+\sqrt{6})(\sqrt{3}-\sqrt{2})}{(\sqrt{3})^2-(\sqrt{2})^2}\\\\\rightarrow \frac{(3\sqrt{3}-3\sqrt{2}+\sqrt{6}\sqrt{3}-\sqrt{2}\sqrt{6})}{(1)}\\\\\rightarrow \frac{(3\sqrt{3}-3\sqrt{2}+\sqrt{3}\sqrt{2}\sqrt{3}-\sqrt{2}\sqrt{2}\sqrt{3})}{(1)}\\\\\rightarrow (3\sqrt{3}-3\sqrt{2}+3\sqrt{2}-2\sqrt{3})\\\\\rightarrow (3\sqrt{3}-2\sqrt{3})\\\\\rightarrow (\sqrt{3})$

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