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 find what whole number and rational number to the nearest half \( \sqrt{10} \) is between, we first need to approximate \( \sqrt{10} \).

Calculating \( \sqrt{10} \):

1. We know that \( 3^2 = 9 \) and \( 4^2 = 16 \). Therefore, \( \sqrt{10} \) is between 3 and 4.
2. To be more precise, we can estimate by checking halfway points:
- \( 3.1^2 = 9.61 \)
- \( 3.2^2 = 10.24 \)

From this, we see that:

- \( \sqrt{10} \) is between 3.1 and 3.2.

Next, let’s check for a rational number to the nearest half:

1. The nearest half numbers between 3 and 4 are 3.0, 3.5, and 4.0.
2. Since \( \sqrt{10} \) is approximately 3.16, it rounds to 3.0 or 3.5.

Thus, we can determine:

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

So in conclusion:

\(\sqrt{10}\) is between **3** (whole number) and **3.5** (rational number to the nearest half).