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

Question

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 less than pi 12 −−−√ >π

Answer 1

To evaluate the statements regarding the square roots and their comparisons with known values or constants, let's analyze each statement one by one.

1. $\sqrt{16}>4$:

   • We calculate $\sqrt{16}=4$.
   • Therefore, this statement is false.

2. $\sqrt{16}<4$:

   • As previously calculated, $\sqrt{16}=4$.
   • Therefore, this statement is also false.

3. $\sqrt{12}<\pi$:

   • We know $\pi \approx 3.14$.
   • $\sqrt{12}\approx 3.464$ (since $\sqrt{12}=\sqrt{4\cdot 3}=2\sqrt{3}$, and $\sqrt{3}\approx 1.732$).
   • Thus $\sqrt{12}>\pi$, making this statement false.

4. $\sqrt{12}>\pi$:

   • As we calculated, $\sqrt{12}\approx 3.464$ and $\pi \approx 3.14$.
   • Therefore, $\sqrt{12}>\pi$ is true.

From the analysis, the statement that is true is:

$\sqrt{12}>\pi$.