To determine which of the given expressions is rational, we first need to understand what a rational number is. A rational number is any number that can be expressed as the quotient or fraction \( \frac{p}{q} \) of two integers \( p \) and \( q \), where \( q \neq 0 \).
Let's analyze each option:
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4.121221222...: This is a non-terminating decimal that appears to have a repeating pattern after the decimal (the "222..." part). Since it is a repeating decimal, it is a rational number.
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Square root of 36: The square root of 36 is 6, which is an integer and hence a rational number.
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Square root of 21: The square root of 21 is not a whole number, and it cannot be expressed as a fraction of two integers, making it an irrational number.
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1.192744502...: This is a non-terminating decimal without an obvious repeating pattern, suggesting it is an irrational number.
Based on this analysis, the expressions that are rational are:
- Square root of 36
- 4.121221222...
Among the options provided, both the square root of 36 and the decimal 4.121221222... are rational. If you need to choose only one, the more straightforward example would be square root of 36, which equals 6.