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 $3.5$.