List the integer of the elements of B = {7, V7, –20, 0, –, 1.5, /16 8 55

Algebra and Trigonometry (6th Edition)
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Author:Robert F. Blitzer
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ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Exercise: Identifying Integers from a Set**

**Instructions:**
List the integers from the elements of the set \( B \).

**Given Set:**
\[ B = \{7, \sqrt{7}, -20, 0, -\frac{5}{8}, \frac{8}{5}, 1.5, \sqrt{16}\} \]

1. **Identify Integers:**
   To determine which elements in the set are integers, look for numbers that do not have a fractional or decimal component, and whose square roots (if applicable) are also integers. 

2. **Solution:**
   - The element \( 7 \) is an integer.
   - The element \( \sqrt{7} \) is not an integer because the square root of 7 is an irrational number.
   - The element \( -20 \) is an integer.
   - The element \( 0 \) is an integer.
   - The element \( -\frac{5}{8} \) is not an integer because it is a fraction.
   - The element \( \frac{8}{5} \) is not an integer because it is a fraction.
   - The element \( 1.5 \) is not an integer because it is a decimal.
   - The element \( \sqrt{16} \) is \(4\), and since 4 is an integer, \( \sqrt{16} \) is considered an integer.

3. **Conclusion:**
   The integers from the set \( B \) are:
   \[ \{7, -20, 0, 4\} \]
Transcribed Image Text:**Exercise: Identifying Integers from a Set** **Instructions:** List the integers from the elements of the set \( B \). **Given Set:** \[ B = \{7, \sqrt{7}, -20, 0, -\frac{5}{8}, \frac{8}{5}, 1.5, \sqrt{16}\} \] 1. **Identify Integers:** To determine which elements in the set are integers, look for numbers that do not have a fractional or decimal component, and whose square roots (if applicable) are also integers. 2. **Solution:** - The element \( 7 \) is an integer. - The element \( \sqrt{7} \) is not an integer because the square root of 7 is an irrational number. - The element \( -20 \) is an integer. - The element \( 0 \) is an integer. - The element \( -\frac{5}{8} \) is not an integer because it is a fraction. - The element \( \frac{8}{5} \) is not an integer because it is a fraction. - The element \( 1.5 \) is not an integer because it is a decimal. - The element \( \sqrt{16} \) is \(4\), and since 4 is an integer, \( \sqrt{16} \) is considered an integer. 3. **Conclusion:** The integers from the set \( B \) are: \[ \{7, -20, 0, 4\} \]
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