To compare \(\sqrt{81}\) and \(\sqrt{88}\), we first calculate \(\sqrt{81}\):
\[ \sqrt{81} = 9 \]
Next, we can estimate \(\sqrt{88}\). Since \(88\) is between \(81\) and \(100\) (where \(\sqrt{100} = 10\)), we know that:
\[ 9 < \sqrt{88} < 10 \]
To get a better approximation for \(\sqrt{88}\), we can calculate it by observing that \(88\) is closer to \(81\) than \(100\). We can use the average of \(9\) and \(10\) to start:
\[ \sqrt{88} \approx 9.4 \quad (\text{since } 9.4^2 = 88.36 \text{ and } 9.3^2 = 86.49) \] \[ \sqrt{88} \approx 9.366 \quad (\text{more accurately, this is closer to the actual value}) \]
Since \(9 < 9.366 < 10\), we confirm:
\[ \sqrt{81} < \sqrt{88} \]
Thus, the correct inequality statement comparing \(\sqrt{81}\) and \(\sqrt{88}\) is:
\[ \sqrt{81} < \sqrt{88} \]
Answer: \(<\)
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