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

1 answer

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:

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