To determine if the product \( \sqrt{75} \cdot \frac{1}{3} \) is rational or irrational, we first analyze the factors involved.
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Understanding the factors:
- \( \sqrt{75} \): The number 75 can be factored into \( 25 \times 3 \), so \( \sqrt{75} = \sqrt{25 \times 3} = \sqrt{25} \times \sqrt{3} = 5\sqrt{3} \). Since \( \sqrt{3} \) is known to be an irrational number, \( \sqrt{75} \) is also irrational.
- \( \frac{1}{3} \): This is a rational number because it can be expressed as the fraction of two integers.
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Analyzing the product:
- The product of a rational number and an irrational number is always irrational.
Based on this reasoning, the correct response is:
It is irrational because one of the factors is irrational.