Using a number line, what whole number and rational number to the nearest half is 105−−−√

Question

between?(1 point)
Responses

between 10 and 10.5
between 10 and 10.5

between 11 and 11.5
between 11 and 11.5

between 9.5 and 10
between 9.5 and 10

between 10.5 and 11

Answer 1

To determine where \( \sqrt{105} \) falls on a number line, we first need to calculate its approximate value.

Calculating \( \sqrt{105} \):

1. We know that \( 10^2 = 100 \) and \( 11^2 = 121 \).
2. This means \( 10 < \sqrt{105} < 11 \).

To get a more accurate estimate, we can determine what \( \sqrt{105} \) is approximately:

• \( 10.2^2 = 104.04 \)
• \( 10.3^2 = 106.09 \)

This means that \( 10.2 < \sqrt{105} < 10.3 \).

Thus, to the nearest half, \( \sqrt{105} \approx 10.2 \), which is between 10 and 10.5.

So the answer is:

between 10 and 10.5.