Using rational approximations, what statement is true? responses 16 −−−√<4 start root 16 end root less than 4 12 −−−√ >π start root 12 end root greater than pi 12 −−−√<π start root 12 end root less than pi 16−−√>4

Answer 1

To evaluate the given inequalities, we need to calculate the square roots and compare them to the values provided.

1. For \( \sqrt{16} < 4 \):

   • \( \sqrt{16} = 4 \)
   • This statement is false since \( 4 \) is not less than \( 4 \).

2. For \( \sqrt{16} > 4 \):

   • \( \sqrt{16} = 4 \)
   • This statement is also false since \( 4 \) is not greater than \( 4 \).

3. For \( \sqrt{12} > \pi \):

   • \( \sqrt{12} \approx 3.464 \)
   • \( \pi \approx 3.14159 \)
   • This statement is true since \( 3.464 > 3.14159 \).

4. For \( \sqrt{12} < \pi \):

   • Since \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14159 \), the statement \( \sqrt{12} < \pi \) is false because \( 3.464 > 3.14159 \).

Therefore, the true statement is:

• \( \sqrt{12} > \pi \).