Question : $\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}}{\sqrt[3]{8}}=?$
Option 1: $4$
Option 2: $2$
Option 3: $8$
Option 4: $\frac{1}{2}$
Correct Answer: $2$
Solution :
Given: $\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+\sqrt{225}}}}}}}{\sqrt[3]{8}}$
$=\frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{154+15}}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{108+\sqrt{169}}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{108+13}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+\sqrt{121}}}}}{2}$
$= \frac{{\sqrt{10+\sqrt{25+11}}}}{2}$
$=\frac{{\sqrt{10+\sqrt{36}}}}{2}$
$= \frac{{\sqrt{10+6}}}{2}$
$=\frac{{\sqrt{16}}}{2}$
$= \frac{4}{2}$
$= 2$
Hence, the correct answer is $2$.
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