A) 4
B) \[14\sqrt{7}\]
C) \[3\sqrt{5}\]
D) \[5\sqrt{3}\]
Correct Answer: C
Solution :
Mean proportion between \[(15+\sqrt{200})\] and \[(27-\sqrt{648})\] \[=\sqrt{(15+\sqrt{200})(27-\sqrt{648})}\] \[=\,\sqrt{(15\times 27)-(15\times \sqrt{648})+27\sqrt{200})}\] \[-\sqrt{(\sqrt{200}\times \sqrt{648})}\] \[=\,\,\sqrt{405-(15\times 18\sqrt{2})+27\times 10\sqrt{2})}\] \[=\,-\sqrt{10\sqrt{2}\times 18\sqrt{2}}\] \[=\,\sqrt{405-180\times 2}\] \[=\,\sqrt{405-360}=\sqrt{45}=\]
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