Discover the answers you need at Westonci.ca, where experts provide clear and concise information on various topics. Connect with a community of experts ready to provide precise solutions to your questions on our user-friendly Q&A platform. Join our platform to connect with experts ready to provide precise answers to your questions in different areas.
Sagot :
To identify which set contains the perfect square integers between 1 and 80 inclusive, we need to determine which numbers are indeed perfect squares within the provided range. A perfect square is an integer that is the square of another integer.
Let's evaluate the sets provided to see which one contains all such perfect squares:
1. The first set is [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64, 80\}\)[/tex]:
- [tex]\(1 = 1^2\)[/tex]
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
- [tex]\(80\)[/tex] is not a perfect square because [tex]\( \sqrt{80} \approx 8.94 \)[/tex] which is not an integer.
2. The second set is [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64\}\)[/tex]:
- [tex]\(1 = 1^2\)[/tex]
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
3. The third set is [tex]\(\{4, 9, 16, 25, 36, 49, 64\}\)[/tex]:
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
- This set is missing [tex]\(1\)[/tex], which is also a perfect square.
After examining the elements, it is clear tha the set [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64\}\)[/tex] correctly lists all the perfect squares up to 80 and does not include any non-perfect squares like 80.
Thus, the correct set of perfect square integers between 1 and 80 inclusive is:
[tex]\[ \{1, 4, 9, 16, 25, 36, 49, 64\} \][/tex]
Let's evaluate the sets provided to see which one contains all such perfect squares:
1. The first set is [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64, 80\}\)[/tex]:
- [tex]\(1 = 1^2\)[/tex]
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
- [tex]\(80\)[/tex] is not a perfect square because [tex]\( \sqrt{80} \approx 8.94 \)[/tex] which is not an integer.
2. The second set is [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64\}\)[/tex]:
- [tex]\(1 = 1^2\)[/tex]
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
3. The third set is [tex]\(\{4, 9, 16, 25, 36, 49, 64\}\)[/tex]:
- [tex]\(4 = 2^2\)[/tex]
- [tex]\(9 = 3^2\)[/tex]
- [tex]\(16 = 4^2\)[/tex]
- [tex]\(25 = 5^2\)[/tex]
- [tex]\(36 = 6^2\)[/tex]
- [tex]\(49 = 7^2\)[/tex]
- [tex]\(64 = 8^2\)[/tex]
- This set is missing [tex]\(1\)[/tex], which is also a perfect square.
After examining the elements, it is clear tha the set [tex]\(\{1, 4, 9, 16, 25, 36, 49, 64\}\)[/tex] correctly lists all the perfect squares up to 80 and does not include any non-perfect squares like 80.
Thus, the correct set of perfect square integers between 1 and 80 inclusive is:
[tex]\[ \{1, 4, 9, 16, 25, 36, 49, 64\} \][/tex]
Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Your questions are important to us at Westonci.ca. Visit again for expert answers and reliable information.