Question

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

Answer 1

To find the whole number and the rational number to the nearest half that \( \sqrt{10} \) (or \( 10^{1/2} \)) is between, we first need to calculate the approximate value of \( \sqrt{10} \).

Calculating \( \sqrt{10} \):

- We know that \( 3^2 = 9 \) and \( 4^2 = 16 \), so \( \sqrt{10} \) is between 3 and 4.
- To get a more precise estimate, we can calculate \( \sqrt{10} \) using a calculator or estimating. It is approximately \( 3.16 \).

Now, we need to find the nearest half:

- The nearest halves around \( 3.16 \) are \( 3.0 \) and \( 3.5 \).

Thus, rounding \( \sqrt{10} \) to the nearest half gives us:
- \( 3.0 \) (the whole number)
- \( 3.0 \) (the rational number to the nearest half)

In conclusion, \( \sqrt{10} \) is between the whole number 3 and the rational number 3.0 (nearest half).