Discussion
If x = \(\sqrt{198} \times \sqrt{550}\) and y = \(\sqrt[3]{99} \times \sqrt[3]{363}\), then \(\dfrac{1}{x} + \dfrac{1}{y}\) is equal to :
Answer: B
The value is 0.0333..., written \(0{\cdot}0\overline{3}\).
\[ \begin{aligned} x &= \sqrt{198 \times 550} = \sqrt{108900} = 330 \\ y &= \sqrt[3]{99 \times 363} = \sqrt[3]{35937} = 33 \\ \frac{1}{x} + \frac{1}{y} &= \frac{1}{330} + \frac{10}{330} \\ &= \frac{11}{330} = \frac{1}{30} \end{aligned} \]
1/30 = 0.0333..., where only the 3 repeats. 0.3333... is 1/3, ten times too large, 0.0101... is 1/99 and 0.111... is 1/9.
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