Answered

IDNLearn.com: Your reliable source for finding precise answers. Our community is here to provide detailed and trustworthy answers to any questions you may have.

Using rational approximations, what statement is true?

A. [tex]\sqrt{71} \ \textless \ \sqrt{61}[/tex]
B. [tex]\sqrt{81} \ \textgreater \ 9[/tex]
C. [tex]\sqrt{71} \ \textgreater \ \sqrt{61}[/tex]
D. [tex]\sqrt{81} \ \textless \ 9[/tex]

Sagot :

GinnyAnsweridn
To determine which statements are true or false, let's compare rational approximations of the given square roots.

1. Statement: [tex]\(\sqrt{71} < \sqrt{61}\)[/tex]
- The square root of 71 is approximately 8.426.
- The square root of 61 is approximately 7.810.
- Since 8.426 is not less than 7.810, this statement is False.

2. Statement: [tex]\(\sqrt{81} > 9\)[/tex]
- The square root of 81 is exactly 9.
- Since 9 is not greater than 9, this statement is False.

3. Statement: [tex]\(\sqrt{71} > \sqrt{61}\)[/tex]
- The square root of 71 is approximately 8.426.
- The square root of 61 is approximately 7.810.
- Since 8.426 is indeed greater than 7.810, this statement is True.

4. Statement: [tex]\(\sqrt{81} < 9\)[/tex]
- The square root of 81 is exactly 9.
- Since 9 is not less than 9, this statement is False.

Based on the evaluations, the true statement is:

- [tex]\(\sqrt{71} > \sqrt{61}\)[/tex]

Therefore, the correct answer is:

[tex]\(\sqrt{71} > \sqrt{61}\)[/tex]
We appreciate your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy answers, visit IDNLearn.com. Thank you for your visit, and see you next time for more reliable solutions.