Using rational approximations, what is an inequality statement comparing 81−−√ and 8–√8 ? Enter <, >, or =.(1 point) The inequality is: 81−−√ 8–√8 .

Answer 1

To compare $\sqrt{81}$ and $\sqrt{8}$:

First, we compute $\sqrt{81}$:

$$\sqrt{81}=9$$

Next, we compute $\sqrt{8}$:

$$\sqrt{8}=\sqrt{4\times 2}=\sqrt{4}\times \sqrt{2}=2\sqrt{2}$$

Now, we need to find the approximate value of $\sqrt{2}$:

$$\sqrt{2}\approx 1.414$$

Then,

$$2\sqrt{2}\approx 2\times 1.414\approx 2.828$$

Now, we compare the values:

$$9\text{ (from }\sqrt{81}\text{) }>2.828\text{ (from }\sqrt{8}\text{)}$$

Thus, the inequality is:

$$\sqrt{81}>\sqrt{8}$$

The inequality statement comparing $\sqrt{81}$ and $\sqrt{8}$ is:

$$\sqrt{81}>\sqrt{8}$$

So, the final answer is:

\[

\]