To determine which number is irrational, let's evaluate each option:
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6√: This expression seems incomplete, but if it's intended to mean \( 6\sqrt{a} \) where \( a \) is a positive integer that isn't a perfect square (like 6), then it could be irrational. However, if it represents \( 6\sqrt{6} \), this too would be irrational because the square root of a non-perfect square is irrational.
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Square root of 6: This is indeed an irrational number because 6 is not a perfect square.
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13: This is a whole number and is rational.
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1 over 3: This is \( \frac{1}{3} \), which is also a rational number.
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0.14¯¯¯¯ (0.14 with a bar over 14): This represents the repeating decimal 0.141414…, which is a rational number.
Based on this analysis, the square root of 6 is the only irrational number listed.