To determine which of the given options is rational, let's analyze each one:
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13√: This is \( 13\sqrt{3} \). Since it is a product of a rational number (13) and an irrational number (\(\sqrt{3}\)), it is irrational.
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The fraction with numerator 1 and denominator square root of 3: This is expressed as \( \frac{1}{\sqrt{3}} \). Since the denominator is an irrational number, this fraction is also irrational.
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3 −−√ × 3–√: This can be interpreted as \( \sqrt{3} \times \sqrt{3} = 3\). The product of \(\sqrt{3}\) with itself yields a rational number (3).
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3√1: This can be interpreted as \(\sqrt{3} \cdot 1\), which is \( \sqrt{3} \). This is an irrational number.
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The fraction with numerator square root of 3 and denominator 1: This fraction is \( \frac{\sqrt{3}}{1} = \sqrt{3} \), which is irrational.
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3–√ + 3–√: This represents \( \sqrt{3} + \sqrt{3} = 2\sqrt{3} \). Since it is a rational number (2) multiplied by an irrational number (\(\sqrt{3}\)), it is also irrational.
The only rational number in the options is:
3 −−√ × 3–√ = 3.