An irrational number is a number that cannot be expressed as a simple fraction, meaning it cannot be written in the form \( \frac{a}{b} \) where \( a \) and \( b \) are integers and \( b \neq 0 \).
Let's analyze each option:
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−15/29: This is a rational number because it can be expressed as a fraction of two integers.
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0.343434...: This is a repeating decimal (specifically \( 0.\overline{34} \)), and it can also be expressed as a fraction. Therefore, it is rational.
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\( 2\sqrt{3} \): The square root of 3 is an irrational number (it cannot be expressed as a fraction). Multiplying it by 2 still results in an irrational number. Thus, \( 2\sqrt{3} \) is irrational.
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87.9821: This is a decimal and can be expressed as a fraction (\( \frac{879821}{10000} \)). Therefore, it is a rational number.
From this analysis, the only irrational number among the options provided is:
\( 2\sqrt{3} \).
6 answers