The expression you provided, \( \sqrt{25} \), simplifies to 5.
To determine the smallest subset that the number 5 fits into, we can consider various sets of numbers:
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Natural Numbers: The set of natural numbers includes all positive integers (1, 2, 3, ...). Since 5 is a positive integer, it belongs to this set.
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Whole Numbers: This set includes all natural numbers and the number 0. Hence, 5 fits into this set as well.
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Integers: The set of integers includes all whole numbers and their negatives (..., -3, -2, -1, 0, 1, 2, 3, ...). 5 is also included in this set.
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Rational Numbers: The set of rational numbers includes all numbers that can be expressed as the quotient of two integers. Since 5 can be written as \( \frac{5}{1} \), it fits into this subset too.
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Real Numbers: The set of real numbers consists of all rational and irrational numbers. Therefore, 5 also belongs to this set.
Given these considerations, the smallest set that includes the number 5 is:
Natural Numbers \( \mathbb{N} \) (which includes only positive integers).
So, the answer is that the smallest subset is the set of Natural Numbers.