Using rational approximations, what statement is true?

Question

options:

√16 < 4

√12 > π

√16 > 4

√12 < π

Answer 1

To evaluate the statements using rational approximations, let's calculate and compare the values.

1. √16 < 4:

   • √16 = 4
   • So, √16 < 4 is false.

2. √12 > π:

   • We know that π is approximately 3.14.
   • √12 is approximately 3.464 (since √12 = √(4*3) = 2√3, and √3 is approximately 1.732).
   • 3.464 is greater than 3.14, so √12 > π is true.

3. √16 > 4:

   • As calculated earlier, √16 = 4.
   • So, √16 > 4 is false.

4. √12 < π:

   • As we found that √12 is approximately 3.464, and π is approximately 3.14.
   • Therefore, √12 < π is false.

From these evaluations, the true statement is:

√12 > π.