Which inequalities are true? Select the three correct answers.(3 points)

Question

Responses
6–√<2–√6<2
6–√<2–√6<2
9–√<12−−√9<12
9–√<12−−√9<12
8–√>28>2
square root of 8 is greater than 2
0<5–√0<5
0<5–√0<5
8–√>8

Answer 1

To determine which inequalities are true among the provided options, let's evaluate each statement:

1. √6 < 2 - √6 < 2

   • First, evaluate √6:√6 is approximately 2.45.
   • Evaluating the inequality:
     • Left part: √6 < 2. False.
     • Middle part: 2 - √6 is about 2 - 2.45 = -0.45 (which is less than 2, but not a valid statement since the first part is false).

2. √9 < √12 < 9

   • Evaluate:
     • √9 = 3
     • √12 = 3.46 (approximately).
   • The inequality is:
     • 3 < 3.46 < 9, which is true.

3. √8 > 28 > 2

   • Evaluate:
     • √8 is approximately 2.83, and the statement says: 2.83 > 28, which is false. Therefore, this entire inequality is false.

4. 0 < √5 < 0

   • This statement can be evaluated:
     • √5 is approximately 2.24.
   • It means: 0 < 2.24 (true), but 2.24 < 0 (false). So this inequality is false.

5. √8 > 8

   • Evaluate:
     • √8 is approximately 2.83, which is certainly not greater than 8. This statement is false.

Only the second statement is true. Now, looking again closely at the options they have given, they seem to mention the same inequality multiple times with a specific structure but possibly incorrect interpretation.

So, the valid inequalities correctly identified are:

• √9 < √12 < 9 (This is the only correct inequality based on standard arithmetic operations).

There seem to be no other inequalities repeating correctly based roughly on an incorrect misplacement or redundancy in the structure, thus choose the appropriate choice one where valid and correct.

The answer can be concluded to summarize singularly: True Inequality is:

• √9 < √12 < 9.

Let me know if further clarification is needed!