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Using rational approximations,what statement is true?

A.Square root 81 < 9
B.square root 71 < square root 61
C.Square root 81 < 9
D.Square root 71<square root 61

5 answers

Let's analyze each of the statements:

A. \(\sqrt{81} < 9\)
This statement is false because \(\sqrt{81} = 9\), so \(9 < 9\) is not true.

B. \(\sqrt{71} < \sqrt{61}\)
This statement is false because \(\sqrt{71} > \sqrt{61}\).

C. \(\sqrt{81} < 9\)
This is the same statement as A and is also false for the same reason.

D. \(\sqrt{71} < \sqrt{61}\)
This is again the same as B and is false.

Based on the analysis above, it looks like I misspoke regarding options B and D—they were just worded the same way, but both indeed state falsehood.

Therefore, the true statement is: None of the above statements are true.

Pick the most true one

Upon reevaluating the statements with the goal of identifying the "most true" one, here they are again for clarity:

A. \(\sqrt{81} < 9\)
B. \(\sqrt{71} < \sqrt{61}\)
C. \(\sqrt{81} < 9\) (same as A)
D. \(\sqrt{71} < \sqrt{61}\) (same as B)

Here's the breakdown one more time:

  • A (\(\sqrt{81} < 9\)) is false because \(\sqrt{81} = 9\).
  • B (\(\sqrt{71} < \sqrt{61}\)) is false because \(\sqrt{71} > \sqrt{61}\).
  • C is false for the same reason as A.
  • D is false for the same reason as B.

Since all statements are false, none can be considered "true." However, if you are looking for the "least false" or the "most true," it would be option A or C, because while they are technically false, they state a comparison that is mathematically meaningful but equal.

Thus, if you had to choose one that does not outright misinform but rather misrepresents an equality, A or C would be the less incorrect options.

Choose the most true one

Given the context and the request for the "most true" statement, the best choice would be:

A. \(\sqrt{81} < 9\) (same as C)

Although it is technically false (since \(\sqrt{81} = 9\)), it is not as misleading as the others. The other statements (B and D) suggest an incorrect inequality about square roots, stating that a higher square root is less than a lower square root, which is more fundamentally flawed.

Therefore, the most "true" statement among the options provided is A or C.