Using rational approximations, what statement is true?

Question

responses

√16 > 4

√12 < π

√16 < 4

√12 > π

Answer 1

To evaluate the statements, we can calculate the values of the square roots and compare them with π.

1. √16 > 4:

   • √16 = 4
   • This statement is false; 4 is not greater than 4.

2. √12 < π:

   • √12 ≈ 3.464 (since √12 = √(4*3) = 2√3 and √3 ≈ 1.732)
   • π ≈ 3.14
   • This statement is true; 3.464 is less than 3.14.

3. √16 < 4:

   • As calculated, √16 = 4.
   • This statement is false; 4 is not less than 4.

4. √12 > π:

   • As calculated, √12 ≈ 3.464 and π ≈ 3.14.
   • This statement is false; 3.464 is not greater than 3.14.

Based on these evaluations, the true statement is:

√12 < π.

Answer 2

what’s the right answwr

Answer 3

Apologies for the confusion in my previous explanation. Let's re-evaluate the statements correctly:

1. √16 > 4:

   • √16 = 4.
   • This statement is false.

2. √12 < π:

   • √12 ≈ 3.464 (since √12 = 2√3 and √3 ≈ 1.732).
   • π ≈ 3.14.
   • This statement is true because 3.464 (√12) is greater than 3.14 (π), incorrect in my previous message.

3. √16 < 4:

   • Again, √16 = 4.
   • This statement is false.

4. √12 > π:

   • As previously calculated, √12 ≈ 3.464, which is less than π ≈ 3.14.
   • This statement is false.

So, the correct analysis shows that:

• The true statement is: √12 > π is false; rather, √12 < π is the true statement.

Therefore, the accurate conclusion based on rational approximations is:

√12 < π is true.