Using rational approximations, what is an inequality statement comparing square root 81 and square root 88? Enter <, >, or =

Answer 1

To compare \(\sqrt{81}\) and \(\sqrt{88}\), we can calculate the square roots:

\[ \sqrt{81} = 9 \]

Next, we approximate \(\sqrt{88}\). We know that:

• \(\sqrt{81} = 9\)
• \(\sqrt{100} = 10\)

Since \(88\) is between \(81\) and \(100\), we can deduce that \(\sqrt{88}\) is between \(9\) and \(10\). To estimate further, we can check the squares of numbers closer to \(88\):

• \(9.3^2 = 86.49\)
• \(9.4^2 = 88.36\)

This shows that \(\sqrt{88}\) is between \(9.3\) and \(9.4\), but closer to \(9.4\).

Thus, we can conclude:

\[ \sqrt{81} < \sqrt{88} \]

Therefore, the inequality statement comparing \(\sqrt{81}\) and \(\sqrt{88}\) is:

\[ \sqrt{81} < \sqrt{88} \]

So the answer is:

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