Discussion
If \(\sqrt{15} = 3.8729\), evaluate \((\sqrt{5}+\sqrt{3})/(\sqrt{5}-\sqrt{3})\)
Answer: C
The value is 7.8729.
Rationalise by multiplying the top and bottom by \(\sqrt{5}+\sqrt{3}\):
\[ \begin{aligned} \frac{\sqrt{5}+\sqrt{3}}{\sqrt{5}-\sqrt{3}} &= \frac{(\sqrt{5}+\sqrt{3})^{2}}{5 - 3} \\ &= \frac{8 + 2\sqrt{15}}{2} = 4 + \sqrt{15} \\ &= 4 + 3.8729 = 7.8729 \end{aligned} \]
6.8729 and 8.8729 are off by one in the whole number (3 + \(\sqrt{15}\) and 5 + \(\sqrt{15}\)), and 4.7289 scrambles the digits.
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