To find the product of \( 5 - \sqrt{5} \) and \( \frac{1}{6} \), we first compute the product:
\[ (5 - \sqrt{5}) \cdot \frac{1}{6} = \frac{5 - \sqrt{5}}{6} \]
Next, we need to analyze this expression. The term \( 5 - \sqrt{5} \) includes \( \sqrt{5} \), which is an irrational number. Thus, the entire expression \( 5 - \sqrt{5} \) is also an irrational number because the difference between a rational number (5) and an irrational number (\( \sqrt{5} \)) is irrational.
Now, dividing an irrational number by a rational number (in this case, \( \frac{1}{6} \)) results in an irrational number.
Therefore, the product \( \frac{5 - \sqrt{5}}{6} \) is an irrational number.
The final answer is:
0.3726 . . . ; an irrational number
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