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# Algebra

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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.

Nov 13, 2021

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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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Nov 13, 2021