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

Responses

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

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

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

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

To determine which statement is true, we can evaluate the square root of 12 and the square root of 16, and compare them with π (approximately 3.14) and 4.

  1. Calculate \(\sqrt{12}\): \[ \sqrt{12} \approx 3.464 \] We compare \(3.464\) with \(\pi\) (approximately \(3.14\)): \[ 3.464 > 3.14 \quad (\text{So } \sqrt{12} > \pi) \]

  2. Calculate \(\sqrt{16}\): \[ \sqrt{16} = 4 \] We compare \(4\) with \(4\): \[ 4 = 4 \quad (\text{So } \sqrt{16} \text{ is neither less than nor greater than } 4) \]

Based on these evaluations, we find:

  • \(\sqrt{12} > \pi\)
  • \(\sqrt{16} = 4\) (not less than and not greater than)

The correct statement is: \[ \sqrt{12} > \pi \]

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