Question

Using rational approximations, what statement is true?(1 point)%0D%0AResponses%0D%0A%0D%0A12 −−−√ >π%0D%0Astart root 12 end root greater than pi%0D%0A%0D%0A16−−√>4%0D%0Astart root 16 end root greater than 4%0D%0A%0D%0A16 −−−√<4%0D%0Astart root 16 end root less than 4%0D%0A%0D%0A12 −−−√<π

Answer 1

To evaluate the inequalities, let's calculate the values of the square roots and compare them with the approximate value of π (which is approximately 3.14).

1. For \( \sqrt{12} \): \[ \sqrt{12} \approx 3.464 \]

   • This means \( \sqrt{12} > \pi \), so the statement \( \sqrt{12} < \pi \) is false.

2. For \( \sqrt{16} \): \[ \sqrt{16} = 4 \]

   • This means \( \sqrt{16} > 4 \) is false, and \( \sqrt{16} < 4 \) is also false.

Now we can summarize:

• \( \sqrt{12} > \pi \) is true.
• \( \sqrt{16} > 4 \) is false.
• \( \sqrt{16} < 4 \) is false.
• \( \sqrt{12} < \pi \) is false.

Therefore, the only true statement is: \[ \sqrt{12} > \pi. \]