Question

Find the value of $\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}+\left(\sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}}\right)÷\sqrt{\frac{16}{81}}$

• A. $\frac{31}{3}$
• B. $\frac{54}{7}$
• C. $\frac{108}{13}$
• D. $\frac{69}{16}$

Answer 1

The correct option is D $\frac{69}{16}$

$\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}+\left(\sqrt{\frac{225}{729}}-\sqrt{\frac{25}{144}}\right)÷\sqrt{\frac{16}{81}}=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}+\left(\frac{15}{27}-\frac{5}{12}\right)÷\frac{4}{9}=\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}+\left(\frac{5}{9}-\frac{5}{12}\right)÷\frac{4}{9}=\sqrt{10+\sqrt{25+\sqrt{108+13}}}+\left(\frac{20-15}{36}\right)÷\frac{4}{9}=\sqrt{10+\sqrt{25+\sqrt{121}}}+\left(\frac{5}{36}\right)÷\frac{4}{9}=\sqrt{10+\sqrt{25+11}}+\frac{5}{36}÷\frac{4}{9}=\sqrt{10+\sqrt{36}}+\frac{5}{36}\times \frac{9}{4}=\sqrt{10+6}+\frac{5}{16}=\sqrt{16}+\frac{5}{16}=4+\frac{5}{16}=\frac{69}{16}$