Question : What is the positive value of the following expression?
$\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-(8-11) \div(9 \times 5 \div 5 \text { of } 3)\}]}$
Option 1: $1 \frac{5}{6}$
Option 2: $1 \frac{1}{5}$
Option 3: $2 \frac{4}{5}$
Option 4: $2 \frac{3}{5}$
Correct Answer: $1 \frac{1}{5}$
Solution :
Given: $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-(8-11) \div(9 \times 5 \div 5 \text { of } 3)\}]}$
= $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-(-3) \div(9 \times \frac{5}{15})\}]}$
= $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-\frac{(-3)}{3}\}]}$
= $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text { of }\{29-(-1)\}]}$
= $\sqrt{36 \div 15 \text { of } 2 \text { of }[25 \times 4 \div 4 \text{ of }30]}$
= $\sqrt{36\div15\text{ of } 2 \text{ of }[25 \times \frac{4}{120}]}$
= $\sqrt{36\div 15\text{ of } 2 \text{ of }[25 \times \frac{1}{30}]}$
= $\sqrt{\frac{36}{15 \times 2 \times\frac{5}{6}}}$
= $\sqrt{\frac{36}{25}}$
= $\frac{6}{5}$
= $1 \frac{1}{5}$
Hence, the correct answer is $1 \frac{1}{5}$.
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