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

Question

Responses

16 −−−√<4
start root 16 end root less than 4

12 −−−√<π
start root 12 end root less than pi

16−−√>4
start root 16 end root greater than 4

12 −−−√ >π
start root 12 end root greater than pi
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Answer 1

To evaluate the given statements using rational approximations, we can simplify each one:

1. \( \sqrt{16} < 4 \): This is false. \( \sqrt{16} = 4 \), so it is not less than 4.

2. \( \sqrt{12} < \pi \): Approximating \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14159 \), this statement is also false because \( \sqrt{12} > \pi \).

3. \( \sqrt{16} > 4 \): This is false as \( \sqrt{16} = 4\).

4. \( \sqrt{12} > \pi \): As calculated above, \( \sqrt{12} \approx 3.464 \) and \( \pi \approx 3.14159\), making this statement true.

Therefore, the correct statement is:

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