Question

Using a number line, what whole number and rational number to the nearest half is 97−−√%0D%0A97%0D%0A between?(1 point)%0D%0A97−−√%0D%0A97%0D%0A is between and

Answer 1

that's right 9.5 and 10

Answer 2

To find the interval in which \(\sqrt{97}\) lies, we can first approximate \(\sqrt{97}\). Since \(9^2 = 81\) and \(10^2 = 100\), we know:

\[
9 < \sqrt{97} < 10
\]

Next, we can calculate \(\sqrt{97}\) more precisely. Using a calculator:

\[
\sqrt{97} \approx 9.8489
\]

Now we want to find whole numbers and rational numbers to the nearest half that \(\sqrt{97}\) is between.

The whole numbers that \(\sqrt{97}\) is between are 9 and 10.

To find the nearest half, we can round \(9.8489\) to the nearest half. The nearest half to \(9.8489\) is \(9.5\).

Putting this together, we have:

\(\sqrt{97}\) is between **9** and **10**, and to the nearest half, it is between **9.5** and **10**.

In summary:

\[
\sqrt{97} \text{ is between } 9 \text{ (whole number) and } 9.5 \text{ (rational number to the nearest half).}
\]

Answer 3

Great! To summarize:

- The whole number between which \(\sqrt{97}\) lies is **9** and **10**.
- The rational number to the nearest half is **9.5**.

If you have any more questions or need further assistance, feel free to ask!