Question

2 root2 +5 root 3 + root 2 _ 3 root 3

Answer 1

Answer:

$2 \sqrt{2 } + 5 \sqrt{3} + \sqrt{2} - 3 \sqrt{3 } \\ = 3 \sqrt{2} + 2 \sqrt{3}$

Answer 2

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$2 \sqrt{2} + 5 \sqrt{3} + \frac{ \sqrt{2} }{3 \sqrt{3} }$

$\frac{2 \sqrt{2} \times 3 \sqrt{3} }{1 \times 3 \sqrt{3} } + \frac{5 \sqrt{3} \times 3 \sqrt{3} }{3 \sqrt{3} } + \frac{ \sqrt{2} }{3 \sqrt{3} }$

$\frac{6 \sqrt{6} }{3 \sqrt{3} } + \frac{45}{3 \sqrt{3} } + \frac{ \sqrt{2} }{3 \sqrt{3} }$

$\frac{6 \sqrt{6} + 45 + \sqrt{2} }{3 \sqrt{3} }$

$\frac{(6 \sqrt{6} + 45 + \sqrt{2})( \sqrt{3} )}{(3 \sqrt{3} )( \sqrt{3}) }$

$\frac{6 \sqrt{18} + 45 \sqrt{3} + \sqrt{6} }{9}$