To determine which of the provided numbers is irrational, let's evaluate each one:
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8√: This appears to be "8 times the square root of some number." Since the square root of a non-perfect square is irrational (like \( \sqrt{2}, \sqrt{3}, \) etc.), but if it's interpreted as \( 8\sqrt{n} \) with \( n \) being a perfect square (like \( 4 \) or \( 16 \)), it could be rational. Without that information, we cannot classify it reliably.
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Square root of 8: The square root of 8 can be simplified to \( 2\sqrt{2} \). Since \( \sqrt{2} \) is irrational, \( \sqrt{8} \) is also irrational.
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0.46: This is a terminating decimal number, which is rational. It can be expressed as a fraction (46/100).
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100√3: This is 100 times the square root of 3. Since \( \sqrt{3} \) is irrational, multiplying it by 100 keeps it irrational.
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0.8¯: This represents a repeating decimal, specifically \( 0.888...\), which can be expressed as \( 8/9 \), making it a rational number.
Considering these evaluations, the numbers that are irrational are:
- Square root of 8
- 100√3
However, since the original question asks for "which number is irrational?" and does not allow multiple choices, the most straightforward answer indicating irrationality is:
Square root of 8 (as this is recognized clearly as irrational without needing to consider more complexities).