Question

Using rational approximations, what is an inequality statement comparing 81−−√ and 88–√ ? Enter <, >, or =

Answer 1

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

\[
\sqrt{81} = 9
\]

Now, we can estimate \(\sqrt{88}\). Knowing that \(88\) is close to \(81\) and \(100\), we can find:

\[
\sqrt{88} \approx 9.38
\]

(We can confirm this by noting that \(9.3^2 = 86.49\) and \(9.4^2 = 88.36\), which implies that \(9.3 < \sqrt{88} < 9.4\)).

Thus, we have:

\[
\sqrt{81} = 9 < \sqrt{88} \approx 9.38
\]

So, we have the inequality:

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

The complete statement is:

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

Therefore, the answer is:

\(<\)