CTET Paper II (Mathematics and Science) 10 Jan 2023 Solved Paper

Concept:Convert decimals to fractions, simplify under the square root by cancelling powers of 10, then take square roots of perfect squares.Explanation:Write each decimal as a fraction: $0.081 = \frac{81}{1000}$, $2.5 = \frac{25}{10}$, $3.24 = \frac{324}{100}$, $0.0625 = \frac{625}{10000}$, $7.29 = \frac{729}{100}$.Combine inside the square root: $\sqrt{\frac{\frac{81}{1000} \times \frac{25}{10} \times \frac{324}{100}}{\frac{625}{10000} \times \frac{729}{100}}}$.Multiply numerator and denominator separately. Powers of 10 in numerator: $1000 \times 10 \times 100 = 10^6$, denominator: $10000 \times 100 = 10^6$. They cancel.Now take square roots of perfect squares: $\sqrt{81}=9$, $\sqrt{25}=5$, $\sqrt{324}=18$, $\sqrt{625}=25$, $\sqrt{729}=27$.So the expression becomes $\frac{9 \times 5 \times 18}{25 \times 27}$. Simplify: numerator $9 \times 5 = 45$, $45 \times 18 = 810$. Denominator $25 \times 27 = 675$. Then $\frac{810}{675} = 1.2$.Answer:$1.2$, which is option B.