Задание 12, стр 22

Question

Вычислите.
$$a)  \sqrt{2} \cdot \sqrt{0,(2)} \quad b)  \sqrt{0 .(2)} \cdot \sqrt{0,(8)} \quad c)  \frac{\sqrt{13}}{\sqrt{1,(4)}}  \quad d) \frac{\sqrt{1,(7)}}{\sqrt{0,(4)}} $$

Gimli · Accepted Answer

\begin{enumerate}[label=(alph*)]
\item $$\sqrt{2}\cdot \sqrt{0.(2)} = \sqrt{2}\cdot \sqrt{\frac{2}{9}} = \sqrt{2}\cdot \frac{\sqrt{2}}{\sqrt{9}} = \sqrt{2}\cdot \frac{\sqrt{2}}{3} = \frac{\sqrt{2}\cdot \sqrt{2}}{3} = \frac{2}{3}.$$
\item $$\sqrt{0.(2)}\cdot \sqrt{0.(8)} = \sqrt{\frac{2}{9}}\cdot \sqrt{\frac{8}{9}} = \frac{\sqrt{2}}{\sqrt{9}}\cdot \frac{\sqrt{8}}{\sqrt{9}} = \frac{\sqrt{2}\cdot \sqrt{8}}{\sqrt{9}\cdot \sqrt{9}} = \frac{\sqrt{16}}{9} = \frac{4}{9}.$$
\item $$\frac{\sqrt{13}}{\sqrt{1.(4)}} = \sqrt{\frac{13}{1,(4)}} = \sqrt{\frac{13}{\frac{13}{9}}} = \sqrt{13\cdot \frac{9}{13}} = \sqrt{9} = 3.$$
\item $$\frac{\sqrt{1.(7)}}{\sqrt{0.(4)}} = \sqrt{\frac{1.(7)}{0.(4)}} = \sqrt{\frac{\frac{16}{9}}{\frac{4}{9}}} = \sqrt{\frac{16}{9}\cdot \frac{9}{4}} = \sqrt{4} = 2.$$
\end{enumerate}

Задание 12, стр 22

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Задание 12, стр 22

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