Question

Using a number line, what is the approximate value of √ 19?(1 point)
Responses

4.5
4.5

4.25
4.25

4.38
4.38

4.13

Answer 1

To approximate the value of \( \sqrt{19} \) using a number line, we can start by identifying two perfect squares between which 19 lies. The perfect squares around 19 are:

- \( 4^2 = 16 \)
- \( 5^2 = 25 \)

Since \( 16 < 19 < 25 \), we know that:

\[
4 < \sqrt{19} < 5
\]

Next, we can check the decimal values between 4 and 5 to narrow it down further:

- \( 4.5^2 = 20.25 \) (which is greater than 19)
- \( 4.4^2 = 19.36 \) (which is also greater than 19)
- \( 4.3^2 = 18.49 \) (which is less than 19)
- \( 4.38^2 \approx 19.0644 \) (which is slightly greater than 19)
- \( 4.35^2 = 18.9225 \) (which is less than 19)

From these calculations, we can see that \( \sqrt{19} \) is between 4.35 and 4.4 and is closer to 4.38.

Therefore, the best approximate value of \( \sqrt{19} \) from the provided options is:

**4.38**