Using a number line, what whole number and rational number to the nearest half is 10−−√

Question

between?(1 point)
10−−√
is between
and

Answer 1

To find the whole number and the rational number (to the nearest half) that \(\sqrt{10}\) is between, we first calculate the approximate value of \(\sqrt{10}\).

Since \(3^2 = 9\) and \(4^2 = 16\), we know:

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

Now let's find the decimal approximation:

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

Next, we want to find the nearest half. 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 round \(3.162\) to \(3.0\).

Now, we summarize our findings:

• The whole number that \(\sqrt{10}\) is between is 3.
• The rational number to the nearest half that \(\sqrt{10}\) is between is 3.0.

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