Question

$6 \div 3 \sqrt{2 - 2 \sqrt{3 = 3 \sqrt{2 - a \sqrt{3} } }$
find a? ​

Answer 1

Step-by-step explanation:

$</p><p>6 \div 3 \sqrt{2} - 2 \sqrt{3} = 3 \sqrt{2 }- a \sqrt{3} \\ \sqrt{2} - 2 \sqrt{3} = 3 \sqrt{2 }- a \sqrt{3} \\ a \sqrt{3} = 3 \sqrt{2} - \sqrt{2} + 2 \sqrt{3} \\ a \sqrt{3} = 2 \sqrt{2} + 2 \sqrt{3} \\ a = \frac{2 \sqrt{2} +2 \sqrt{3} }{ \sqrt{3} } \\ a = \frac{(2 \sqrt{2} +2 \sqrt{3}) \times \sqrt{3} }{ \sqrt{3} \times \sqrt{3} } \\ a = \frac{2 \sqrt{6} + 6}{3} \\ a = \frac{2 \sqrt{3} ( \sqrt{2 } + \sqrt{3} )}{3}$