A) \[\frac{69}{16}\]
B) \[\frac{54}{7}\]
C) \[\frac{31}{3}\]
D) \[\frac{108}{13}\]
Correct Answer: A
Solution :
We have, \[\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}\] \[+\left( \sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}} \right)\div \sqrt{\frac{16}{81}}\] \[=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}\] \[+\left( \frac{15}{27}-\frac{5}{12} \right)\div \left( \frac{4}{9} \right)\] \[=\sqrt{10+\sqrt{25+\sqrt{108+13}}}+\left( \frac{60-45}{108} \right)\div \frac{4}{9}\] \[=\sqrt{10+\sqrt{25+11}}+\frac{15}{108}\times \frac{9}{4}=\sqrt{10+6}+\frac{5}{16}\] \[=4+\frac{5}{16}=\frac{64+5}{16}=\frac{69}{16}\]
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