TIP: You can click the calculator symbol at the top of the screen to bring up Desmos at any time!The Venn diagram below shows the relationship among several sets of numbers.

Question

Where should `-\sqrt{169}`be placed in the Venn diagram?Where should `-\sqrt{169}`be placed in the Venn diagram?

Answer 1

To determine where \(-\sqrt{169}\) should be placed in a Venn diagram of sets of numbers, first calculate the value of \(-\sqrt{169}\):

\[ -\sqrt{169} = -13 \]

Next, we can categorize \(-13\) according to its properties:

1. Natural Numbers: These are positive integers (1, 2, 3, ...). \(-13\) is not a natural number.
2. Whole Numbers: These include all natural numbers and zero (0, 1, 2, 3, ...). \(-13\) is not a whole number.
3. Integers: This set includes all positive and negative whole numbers, as well as zero (..., -2, -1, 0, 1, 2, ...). \(-13\) is an integer.
4. Rational Numbers: This set includes all numbers that can be expressed as a ratio of two integers (a/b, where b ≠ 0). \(-13\) can be expressed as \(-13/1\), so it is a rational number.
5. Real Numbers: This set includes all rational and irrational numbers. \(-13\) is also a real number.

Given these categories, \(-\sqrt{169} = -13\) belongs to the following sets:

• Integers
• Rational Numbers
• Real Numbers

In the Venn diagram, you should place \(-\sqrt{169}\) (or \(-13\)) in the section that represents:

• Integers (which is a subset of Rational and Real Numbers).

If the Venn diagram is structured with circles for Natural Numbers, Whole Numbers, Integers, Rational Numbers, and Real Numbers, \(-13\) would be in the circle for Integers, and it would also fall under Rational Numbers and Real Numbers as well. However, since it is negative, it will not be in the Natural or Whole Numbers sections.