(D). [tex] 10 \sqrt{2} + 4 \sqrt{5} [/tex]
PEMBAHASAN :
[tex] \frac{6 \sqrt{10} }{ \sqrt{5} - \sqrt{2}} = \frac{6 \sqrt{10} }{ \sqrt{5} - \sqrt{2}} \times \frac{ \sqrt{5} + \sqrt{2} }{ \sqrt{5} + \sqrt{2} } [/tex]
[tex] = \frac{(6 \sqrt{10})( \sqrt{5} + \sqrt{2})}{( \sqrt{5} - \sqrt{2})( \sqrt{5} + \sqrt{2})} [/tex]
[tex] = \frac{(6 \sqrt{10})( \sqrt{5}) + (6 \sqrt{10})( \sqrt{2})}{( \sqrt{5})( \sqrt{5}) + ( \sqrt{5})( \sqrt{2}) - (\sqrt{2})( \sqrt{5}) - ( \sqrt{2})( \sqrt{2})} [/tex]
[tex] = \frac{(6 \sqrt{50} + 6 \sqrt{20})}{( \sqrt{25} + \sqrt{10} - \sqrt{10} - \sqrt{4}) } [/tex]
[tex] = \frac{(6 \sqrt{25 \times 2} + 6 \sqrt{4 \times 5}) }{ \sqrt{25} - \sqrt{4} } [/tex]
[tex] = \frac{(6 \times 5 \sqrt{2} + 6 \times 2 \sqrt{5})}{5 - 2} [/tex]
[tex] = \frac{(30 \sqrt{2} + 12 \sqrt{5}) }{3} [/tex]
[tex] = 10 \sqrt{2} + 4 \sqrt{5} [/tex]
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