Question

Using a number line, what is the approximate value of ?
(1 point)
19
−− √
4.25
4.38
4.13
4.5

Answer 1

To approximate the value of \( \sqrt{19} \), we can look for two perfect squares between which 19 lies.

1. The perfect square below 19 is \( 16 \) (since \( 4^2 = 16 \)).
2. The perfect square above 19 is \( 25 \) (since \( 5^2 = 25 \)).

This tells us that:

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

Next, to narrow it down further, we can check the squares of the decimal values around 4.5:

- \( 4.5^2 = 20.25 \) (which is greater than 19)
- \( 4.4^2 = 19.36 \) (still greater than 19)
- \( 4.3^2 = 18.49 \) (which is less than 19)

So we have:

\[
4.3 < \sqrt{19} < 4.4
\]

Now we can look for the value of \( \sqrt{19} \) more precisely by checking 4.35:

- \( 4.35^2 = 18.9225 \) (which is less than 19)
- \( 4.36^2 = 19.0496 \) (which is greater than 19)

So now we know:

\[
4.35 < \sqrt{19} < 4.36
\]

Thus, the approximate value of \( \sqrt{19} \) is closer to:

- \( 4.35 \)

From the provided options:

- 4.25
- 4.38
- 4.13
- 4.5

The value that is closest to \( \sqrt{19} \) is **4.38**.

Therefore, the approximate value of \( \sqrt{19} \) is **4.38**.