Using a number line, what whole number and rational number to the nearest half is 58−−√

Question

between?(1 point)
Responses

between 7 and 7.5
between 7 and 7.5

between 8 and 8.5
between 8 and 8.5

between 8.5 and 9
between 8.5 and 9

between 7.5 and 8

Answer 1

To determine where \( \sqrt{58} \) falls on the number line, we need to find its approximate value.

Calculating \( \sqrt{58} \):

1. We know that \( 7^2 = 49 \) and \( 8^2 = 64 \).
2. Therefore, \( 7 < \sqrt{58} < 8 \).

To get a more precise estimate, we can try calculating a decimal approximation for \( \sqrt{58} \):

• Using a calculator, \( \sqrt{58} \approx 7.615 \).

Now, let's determine which range this number falls into:

• \( 7.5 < 7.615 < 8\)

Thus, \( \sqrt{58} \) is between 7.5 and 8.

Now rounding 7.615 to the nearest half gives us 7.5.

Therefore, the answer is:

between 7.5 and 8.