Using rational approximations, what is an inequality statement comparing π and 8–√? Enter <, >, or =.(1 point)

Question

The inequality is: π
8–√.

Answer 1

To compare \( \pi \) and \( 8 - \sqrt{} \), we can first calculate the values of both expressions.

1. Value of \( \pi \): \[ \pi \approx 3.14159 \]

2. Value of \( 8 - \sqrt{} \): First, we calculate \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \approx 2 \times 1.414 = 2.828 \] Then compute \( 8 - \sqrt{8} \): \[ 8 - \sqrt{8} \approx 8 - 2.828 = 5.172 \]

Now we can compare: \[ 3.14159 < 5.172 \]

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

So the final answer is: \[ \pi < 8 - \sqrt{8} \]