To compare \( \pi \) and \( 8 - \sqrt{8} \), we can first evaluate \( 8 - \sqrt{8} \).
Calculating \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828 \] Then, we compute \( 8 - \sqrt{8} \): \[ 8 - \sqrt{8} \approx 8 - 2.828 \approx 5.172 \]
Now, we will use the approximate value of \( \pi \): \[ \pi \approx 3.14159 \]
Now we can compare the two values: \[ \pi \approx 3.14159 < 5.172 \approx 8 - \sqrt{8} \]
Thus, the inequality statement is: \[ \pi < 8 - \sqrt{8} \]
So, the answer is: \[ < \]