Question

The Number System Unit Test
8 of 158 of 15 Items
Question
Using a number line, what whole number and rational number to the nearest half is 58−−√
between?(1 point)
Responses

between 8.5 and 9
between 8.5 and 9

between 8 and 8.5
between 8 and 8.5

between 7.5 and 8
between 7.5 and 8

between 7 and 7.5

Answer 1

To find the position of \( \sqrt{58} \) on a number line, we first need to determine its approximate value.

Calculating \( \sqrt{58} \):

Since \( 7^2 = 49 \) and \( 8^2 = 64 \), we know that \( \sqrt{58} \) is between 7 and 8.

Now we can check where it is more precisely. We can calculate as follows:

- \( 7.5^2 = 56.25 \) (too low)
- \( 7.6^2 = 57.76 \) (still too low)
- \( 7.7^2 = 59.29 \) (too high)

So, \( \sqrt{58} \) is between \( 7.6 \) and \( 7.7 \).

Since we are asked to provide a response in whole number and rational number to the nearest half, we find:

- The whole number is 7.
- The rational number to the nearest half is 7.5 (since \( 7.6 \) falls between \( 7.5 \) and \( 8 \)).

Therefore, the answer is:

**between 7.5 and 8**.