To determine which of the numbers represent irrational numbers, we need to know the definitions of rational and irrational numbers:
- Rational numbers are numbers that can be expressed as the quotient or fraction of two integers (where the denominator is not zero). This includes integers, finite decimals, and repeating decimals.
- Irrational numbers are numbers that cannot be expressed as a simple fraction. They have non-repeating, non-terminating decimal expansions.
Now, let's evaluate the given options:
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1.3333...: This is a repeating decimal, which can be expressed as the fraction \( \frac{4}{3} \). Therefore, it is a rational number.
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Pi (π): This is a well-known irrational number, as it cannot be expressed as a fraction of two integers. Its decimal representation is non-repeating and non-terminating.
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Square root (without specifying): If this refers to \( \sqrt{2} \), \( \sqrt{3} \), or any square root of a non-perfect square number, then it represents an irrational number. However, if it refers to the square root of a perfect square, like \( \sqrt{4} \), it would be rational.
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4/5: This is a fraction and can be expressed as the decimal 0.8, which is a terminating decimal. Therefore, it is a rational number.
In conclusion, the only clear irrational number from the options given is:
- Pi (π).
If the square root refers to a specific non-perfect square (like \( \sqrt{2} \)), it would also be irrational, but that is not clear from the phrasing provided.