Using rational approximations, what is an an equity statement comparing PI and square root of eight enter more than or less than or equal to so the inequality is PI blank square root of eight

Answer 1

To compare \(\pi\) and \(\sqrt{8}\) using rational approximations, we'll first calculate their approximate numerical values.

1. The value of \(\pi\) is approximately \(3.14\).
2. To find \(\sqrt{8}\), we can simplify it: \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2}. \] The approximate value of \(\sqrt{2}\) is about \(1.414\), so: \[ \sqrt{8} \approx 2 \times 1.414 \approx 2.828. \]

Now, let's compare the two values:

• \(\pi \approx 3.14\)
• \(\sqrt{8} \approx 2.828\)

Since \(3.14 > 2.828\), we can set up the inequality as:

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

So, the complete inequality statement is:

\(\pi > \sqrt{8}\).