Using rational approximations, what is an inequality statement comparing pi and the square root of 8? Enter <, >, or =

Answer 1

To compare \(\pi\) and \(\sqrt{8}\), we can use decimal approximations:

1. The value of \(\pi\) is approximately \(3.14159\).
2. The square root of 8 can be calculated as: \[ \sqrt{8} = \sqrt{4 \cdot 2} = 2\sqrt{2} \] The approximate value of \(\sqrt{2}\) is about \(1.41421\). Therefore, \[ \sqrt{8} \approx 2 \times 1.41421 = 2.82842. \]

Now we can compare:\

\(\pi \approx 3.14159\)

\(\sqrt{8} \approx 2.82842\)

Now we see that:

\[ 3.14159 > 2.82842 \]

Thus, the inequality statement comparing \(\pi\) and \(\sqrt{8}\) is:

\[ \pi > \sqrt{8} \]

So the answer is \(>\).