To compare \( \sqrt{81} \) and \( \sqrt{8} \), we can first calculate the exact values of each.
The value of \( \sqrt{81} \) is: \[ \sqrt{81} = 9 \]
Next, let's determine \( \sqrt{8} \). We can approximate this value: \[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \] Knowing that \( \sqrt{2} \approx 1.414 \): \[ \sqrt{8} \approx 2 \times 1.414 \approx 2.828 \]
Now we can compare: \[ \sqrt{81} = 9 \quad \text{and} \quad \sqrt{8} \approx 2.828 \]
Thus, we have: \[ 9 > 2.828 \]
This leads us to the final comparison: \[ \sqrt{81} > \sqrt{8} \]
Therefore, the inequality statement is: \[ \sqrt{81} > \sqrt{8} \]
In conclusion, the answer is: \[
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