Question

Simplify by Rationalize the denominato 2√6/√2+√3+6√2/√6 +√3-8√3/√6√2.

Answer 1

$\huge {\mathcal{\purple{A}\green{N}\pink{S}\blue{W}\purple{E}\green{R}\pink{!}}}$

$\frac{2 \sqrt{6} }{ \sqrt{2} } + \frac{ \sqrt{3} + 6 \sqrt{2} }{ \sqrt{6} } + \frac{ \sqrt{3} - 8 \sqrt{3} }{ \sqrt{6} \sqrt{2} } \\ \\ = \frac{2 \sqrt{6} \times \sqrt{2} }{ \sqrt{2} \times \sqrt{2} } + \frac{( \sqrt{3} + 6 \sqrt{2}) \times \sqrt{6} }{ \sqrt{6} \times \sqrt{6} } + \frac{ (\sqrt{3} - 8 \sqrt{3} ) \times \sqrt{12} }{ \sqrt{12} \times \sqrt{12} } \\ \\ = \frac{2 \sqrt{12} }{2} + \frac{ \sqrt{18} + 6 \sqrt{12} }{6} + \frac{ \sqrt{36} - 8 \sqrt{36} }{12} \\ \\ = \frac{2 \sqrt{2 \times 2 \times 3} }{2} + \frac{ \sqrt{2 \times 3 \times 3} + 6 \sqrt{2 \times 2 \times 3} }{6} + \frac{ \sqrt{2 \times 2 \times 3 \times 3} - 8 \sqrt{2 \times 2 \times 3 \times 3} }{12} \\ \\ = \frac{4 \sqrt{3} }{2} + \frac{3 \sqrt{2} + 12 \sqrt{3} }{6} + \frac{6 \times 48}{12} \\ \\ = 2 \sqrt{3} + \frac{3( \sqrt{2} + 4 \sqrt{3} )}{6} + 6 \\ \\ = 2 \sqrt{3} + \frac{ \sqrt{2} + 4 \sqrt{3} }{2} + 6 \\ \\ = \frac{4 \sqrt{3} + \sqrt{2} + 4 \sqrt{3} + 12}{2} \\ \\ = \frac{8 \sqrt{3} + \sqrt{2} + 12}{2}$

Hope its helpful ❤️