Question

Using rational approximations, what statement is true?(1 point) Responses 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 greater than pi 12 −−−√<π start root 12 end root less than pi

Answer 1

To evaluate the given statements using rational approximations, let’s analyze each of the square roots and compare them with the specified values.

1. For \( \sqrt{16} \): \[ \sqrt{16} = 4 \] So, the statement \( \sqrt{16} > 4 \) is false, and \( \sqrt{16} < 4 \) is also false.

2. For \( \sqrt{12} \):

   • The approximate value of \( \sqrt{12} \) can be calculated as: \[ \sqrt{12} \approx 3.464 \]
   • The approximate value of \( \pi \) is: \[ \pi \approx 3.14159 \] Therefore, comparing these, we find that: \[ \sqrt{12} \approx 3.464 > 3.14159 \approx \pi \] Thus the statement \( \sqrt{12} > \pi \) is true and \( \sqrt{12} < \pi \) is false.

In conclusion, the true statement is: \[ \sqrt{12} > \pi \]