Question

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:

<