To find out where \(-\sqrt{169}\) should be placed in the Venn diagram, we first need to evaluate the expression.
Calculating \(-\sqrt{169}\): \[ \sqrt{169} = 13 \] Thus, \[ -\sqrt{169} = -13 \]
Now, we need to determine the attributes of \(-13\) in relation to the sets in the Venn diagram. Here are some common sets to consider:
- Natural Numbers: These are positive integers \({1, 2, 3, \ldots}\). \(-13\) is not a natural number.
- Whole Numbers: These are non-negative integers \({0, 1, 2, 3, \ldots}\). \(-13\) is not a whole number.
- Integers: These include all positive and negative whole numbers, as well as zero \({\ldots, -3, -2, -1, 0, 1, 2, 3, \ldots}\). \(-13\) is an integer.
- Rational Numbers: These are numbers that can be expressed as the quotient of two integers, including both integers and fractions. Since \(-13\) can be expressed as \(-13/1\), it is also a rational number.
- Real Numbers: This set includes all rational and irrational numbers. Since \(-13\) is a rational number, it is also a real number.
Since \(-13\) does not belong to the sets of natural or whole numbers but does belong to the sets of integers, rational numbers, and real numbers, we can place \(-13\) in the intersection of the "Integers," "Rational Numbers," and "Real Numbers" in the Venn diagram.
To summarize, \(-\sqrt{169} = -13\) should be placed in the area representing integers, rational numbers, and real numbers, but outside the areas for natural numbers and whole numbers.
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