Question

Using a number line, what whole number and rational number to the nearest half is 10−−√
between?(1 point)
10−−√
is between and .

Answer 1

To determine the range of numbers that \(\sqrt{10}\) (which is \(10^{0.5}\)) falls between, we first need to calculate its approximate value.

The square root of 10 is approximately:

\[
\sqrt{10} \approx 3.162
\]

Next, we want to find the whole numbers it is between:

- The whole number just below \(\sqrt{10}\) is 3.
- The whole number just above \(\sqrt{10}\) is 4.

Thus, we can say:

\[
3 < \sqrt{10} < 4
\]

Next, we determine the nearest half to \(\sqrt{10}\):

- The nearest halves around 3.162 are 3.0 and 3.5. Since 3.162 is closer to 3.0 than to 3.5, we can use these values as well.

Consequently, we find that:

\[
\sqrt{10} \text{ is between } 3 \text{ and } 4, \text{ and between } 3.0 \text{ and } 3.5.
\]

Therefore, your final answer is:

\(\sqrt{10}\) is between \(3\) and \(4\), and between \(3.0\) and \(3.5\).