Question

Simplify 3 root2 - 2root3 ÷ root8 + root27

Answer 1

$= \ \textgreater \ \frac{3 \sqrt{2} - 2 \sqrt{3} }{2 \sqrt{2} + 3 \sqrt{3} }$

$= \ \textgreater \ \frac{3 \sqrt{2} - 2 \sqrt{3} }{2 \sqrt{2} + 3 \sqrt{3} } * \frac{2 \sqrt{2} - 3 \sqrt{3} }{2 \sqrt{2} - 3 \sqrt{3} }$

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

$= \ \textgreater \ \frac{12 - 9 \sqrt{6} - 4 \sqrt{6} + 18 }{8 - 27}$

$= \ \textgreater \ \frac{13 \sqrt{6} + 30 }{-19}$


Hope this helps!