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

1 answer

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:

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