sing rational approximations, what is an inequality statement comparing 81−−√

Question

and 8–√8
? Enter <, >, or =.(1 point)
The inequality is: 81−−√

8–√8
.

Answer 1

To compare \( \sqrt{81} \) and \( 8\sqrt{8} \), we can first calculate their approximate values.

1. Calculate \( \sqrt{81} \): \[ \sqrt{81} = 9 \]

2. Calculate \( 8\sqrt{8} \): First, find \( \sqrt{8} \): \[ \sqrt{8} = \sqrt{4 \times 2} = 2\sqrt{2} \approx 2 \times 1.414 \approx 2.828 \] Now multiply by 8: \[ 8\sqrt{8} \approx 8 \times 2.828 \approx 22.624 \]

Now we can compare: \[ 9 < 22.624 \]

Thus, the inequality is: \[ \sqrt{81} < 8\sqrt{8} \]

So the final answer is: \[ \sqrt{81} < 8\sqrt{8} \]