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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]
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