CTET Paper II (Mathematics and Science) 1 Jan 2022 Solved Paper

Concept:To simplify a division of fractions with square roots, rewrite as multiplication by the reciprocal. Then factor each radicand into a product of a perfect square and another number.Explanation:Start with $\frac{\sqrt{450}}{\sqrt{338}} \div \frac{\sqrt{125}}{\sqrt{245}}$. Change division to multiplication: $\frac{\sqrt{450}}{\sqrt{338}} \times \frac{\sqrt{245}}{\sqrt{125}}$.Factor each square root: $\sqrt{450} = \sqrt{225 \times 2} = 15\sqrt{2}$, $\sqrt{338} = \sqrt{169 \times 2} = 13\sqrt{2}$, $\sqrt{245} = \sqrt{49 \times 5} = 7\sqrt{5}$, $\sqrt{125} = \sqrt{25 \times 5} = 5\sqrt{5}$.Now the expression becomes $\frac{15\sqrt{2}}{13\sqrt{2}} \times \frac{7\sqrt{5}}{5\sqrt{5}}$. Cancel $\sqrt{2}$ and $\sqrt{5}$: $\frac{15}{13} \times \frac{7}{5} = \frac{15 \times 7}{13 \times 5} = \frac{105}{65}$. Simplify by dividing numerator and denominator by 5: $\frac{21}{13}$.Answer:$\frac{21}{13}$, which is option C.