using rational approximations, what is an inequality statement comparing /81 and /88? enter <, >. or =

Question

the inequality is: /81 _ /88

Answer 1

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

\(\sqrt{81} = 9\)

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

\(\sqrt{88} \approx 9.38\) (since \(9^2 = 81\) and \(10^2 = 100\), \(\sqrt{88}\) is between 9 and 10)

Now, we can compare:

\[ 9 < 9.38 \]

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

\(\sqrt{81} < \sqrt{88}\)

So, the answer is:

\(\sqrt{81} < \sqrt{88}\)