Suppose that a, b, and c are real numbers such that a/b = sqrt(10)/sqrt(21) and b/c = sqrt(14)/sqrt(15). Find a/c. Completely simplify and rationalize the denominator.
+9479 a/c = a/b * b/c
\(\frac{a}{c}\ =\ \frac{a}{b}\cdot\frac{b}{c}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt{10}}{\sqrt{21}}\cdot\frac{\sqrt{14}}{\sqrt{15}}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt{10\ \cdot\ 14}}{\sqrt{21\ \cdot\ 15}}\\~\\ \frac{a}{c}\ =\ \sqrt{\frac{10\ \cdot\ 14}{21\ \cdot\ 15}}\\~\\ \frac{a}{c}\ =\ \sqrt{\frac49}\\~\\ \frac{a}{c}\ =\ \frac{\sqrt4}{\sqrt9}\\~\\ \frac{a}{c}\ =\ \frac23\)
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