Question

Using rational approximations, what is an equality statement comparing square root of 81 and square root of 88 enter more than or less than or equal

Answer 1

To compare \(\sqrt{81}\) and \(\sqrt{88}\), we can start by calculating the square root of 81:

\[
\sqrt{81} = 9
\]

Next, we approximate \(\sqrt{88}\). Since \(88\) is between \(81\) (which is \(9^2\)) and \(100\) (which is \(10^2\)), we know that:

\[
9 < \sqrt{88} < 10
\]

To get a better approximation for \(\sqrt{88}\), we can calculate:

\[
\sqrt{88} \approx 9.38 \quad (\text{since } 9.38^2 \approx 88)
\]

Now we have:

\[
\sqrt{81} = 9 \quad \text{and} \quad \sqrt{88} \approx 9.38
\]

Since \(9 < 9.38\), we conclude that:

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

So the equality statement comparing \(\sqrt{81}\) and \(\sqrt{88}\) is:

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