To find the product of \( 5 - \sqrt{5} \) and \( \frac{1}{6} \), first calculate \( 5 - \sqrt{5} \).
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Calculate \( 5 - \sqrt{5} \):
- \( \sqrt{5} \) is approximately \( 2.236 \).
- Thus, \( 5 - \sqrt{5} \approx 5 - 2.236 = 2.764 \).
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Now, multiply \( 5 - \sqrt{5} \) by \( \frac{1}{6} \): \[ \left(5 - \sqrt{5}\right) \times \frac{1}{6} = \frac{5 - \sqrt{5}}{6} \]
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Calculation:
- The approximate value of \( \frac{5 - \sqrt{5}}{6} \):
- \( \frac{2.764}{6} \approx 0.4607 \).
Now, let's determine whether this number is rational or irrational. Since \( \sqrt{5} \) is irrational, it follows that \( 5 - \sqrt{5} \) is also irrational, as the difference between a rational number (5) and an irrational number is always irrational.
Thus, \( \frac{5 - \sqrt{5}}{6} \) is the ratio of an irrational number and a rational number (6), which also results in an irrational number.
So the answer is approximately \( 0.4607 \); an irrational number.
From the given options:
- 0.3726 . . . ; an irrational number
- 2.4027 . . . ; an irrational number
- 2.40; a rational number
- 0.37; a rational number
None of the specific numerical forms match exactly, but based on the analysis, we conclude that it is in the form \( \text{number}; \text{an irrational number} \).
6 answers