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Using rational approximations, what statement is true?

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

Sagot :

GinnyAnsweridn
Let's analyze each statement one by one, using the given results:

1. Statement: [tex]\(\sqrt{81} > 9\)[/tex]
- The square root of 81 is calculated to be 9.0.
- Since 9.0 is equal to 9, the statement [tex]\(\sqrt{81} > 9\)[/tex] is false.

2. 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.
- Comparing these two approximations, we see that 8.426 is not less than 7.810, so the statement [tex]\(\sqrt{71} < \(\sqrt{61}\)[/tex] is false.

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

4. Statement: [tex]\(\sqrt{81} < 9\)[/tex]
- The square root of 81 is 9.0.
- Since 9.0 is equal to 9, the statement [tex]\(\sqrt{81} < 9\)[/tex] is false.

So, the true statement among the given options is:
[tex]\[ \sqrt{71} > \sqrt{61} \][/tex]
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