Question

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Answer 1

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$\frac{1}{2 \sqrt{7} + 3\sqrt{3} }$

$\implies \frac{1(2 \sqrt{7} - 3 \sqrt{3}) }{(2 \sqrt{7} + 3 \sqrt{3})(2 \sqrt{7} - 3 \sqrt{3} )}$

$\implies \frac{2 \sqrt{7} -3 \sqrt{3} }{ {(2 \sqrt{7}) }^{2} - {(3 \sqrt{3}) }^{2} }$

$\implies \frac{2 \sqrt{7} - 3 \sqrt{3} }{(4 \times 7) - (9 \times 3)}$

$\implies \frac{2 \sqrt{7} - 3 \sqrt{3} }{28 - 27}$

$\implies2 \sqrt{7} - 3 \sqrt{3}$

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$\frac{1}{2 \sqrt{7} + 3 \sqrt{3} } = 2 \sqrt{7} - 3 \sqrt{3}$

$2 \sqrt{7} - 3 \sqrt{3} = 4 \sqrt{3} - a \sqrt{2}$

$2 \sqrt{7} + a \sqrt{2} = 4 \sqrt{3} + 3 \sqrt{3}$

$2 \sqrt{7} + a \sqrt{2} = 7 \sqrt{3}$

$a \sqrt{2} = 7 \sqrt{3} - 2 \sqrt{7}$

$a \times \sqrt{2} = 7 \sqrt{3} - 2 \sqrt{7}$

$a = \frac{7 \sqrt{3} - 2 \sqrt{7} }{ \sqrt{2} }$

$a = \frac{ \sqrt{2}(7 \sqrt{3} - 2 \sqrt{7}) }{( \sqrt{2} )( \sqrt{2}) }$

$a = \frac{7 \sqrt{6} - 2 \sqrt{14} }{2}$

$a = \frac{7 \sqrt{6} }{2} - \frac{2 \sqrt{14} }{2}$

$a = 3.5 \sqrt{6} - \sqrt{14}$