Question : Simplify: $\sqrt{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}+\frac{2}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}$
Option 1: $1$
Option 2: $4$
Option 3: $\sqrt{\frac{159}{130}}$
Option 4: $2$
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Correct Answer: $\sqrt{\frac{159}{130}}$
Solution :
$\sqrt{\frac{4\frac{1}{7}-2\frac{1}{4}}{3\frac{1}{2}+1\frac{1}{7}}+\frac{2}{2+\frac{1}{2+\frac{1}{5-\frac{1}{5}}}}}$
= $\sqrt{\frac{\frac{29}{7}-\frac{9}{4}}{\frac{7}{2}+\frac{8}{7}}+\frac{2}{2+\frac{1}{2+\frac{5}{24}}}}$
= $\sqrt{\frac{\frac{53}{28}}{\frac{65}{14}}+\frac{2}{2+\frac{24}{53}}}$
= $\sqrt{\frac{53}{130}+\frac{106}{130}}$
= $\sqrt{\frac{159}{130}}$
Hence, the correct answer is $\sqrt{\frac{159}{130}}$.
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