Question

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

Answer 1

To find where \( \sqrt{10} \) lies on a number line, we first need to calculate its approximate value.

The value of \( \sqrt{10} \) is roughly 3.162.

To determine the whole number it is between, we can observe that:

- \( 3^2 = 9 \) (which is less than 10)
- \( 4^2 = 16 \) (which is greater than 10)

This confirms that \( \sqrt{10} \) is between the whole numbers 3 and 4.

Next, to find the nearest half, we can consider numbers that are spaced in halves:

- 3.0
- 3.5
- 4.0

Since \( 3.162 \) is closer to 3.0 than 3.5, we round \( \sqrt{10} \) to the nearest half, giving us 3.0.

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