Using rational approximations, what statement is true?(1 point)

Question

16−−√>4 start root 16 end root greater than 4 16 −−−√<4 start root 16 end root less than 4 12 −−−√<π start root 12 end root less than pi 12 −−−√ >π

Answer 1

To evaluate the statements regarding the square roots and their comparisons with known values or constants, let's analyze each statement one by one.

1. \( \sqrt{16} > 4 \):

   • We calculate \( \sqrt{16} = 4 \).
   • Therefore, this statement is false.

2. \( \sqrt{16} < 4 \):

   • As previously calculated, \( \sqrt{16} = 4 \).
   • Therefore, this statement is also false.

3. \( \sqrt{12} < \pi \):

   • We know \( \pi \approx 3.14 \).
   • \( \sqrt{12} \approx 3.464 \) (since \( \sqrt{12} = \sqrt{4 \cdot 3} = 2\sqrt{3} \), and \( \sqrt{3} \approx 1.732\)).
   • Thus \( \sqrt{12} > \pi \), making this statement false.

4. \( \sqrt{12} > \pi \):

   • As we calculated, \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14 \).
   • Therefore, \( \sqrt{12} > \pi \) is true.

From the analysis, the statement that is true is:

\( \sqrt{12} > \pi \).