Question

Using a number line, what is the approximate value of √19
?

Answer 1

To find the approximate value of \( \sqrt{19} \) using a number line, we first identify the perfect squares that are close to 19. We know:

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

Since 19 is between 16 and 25, we can conclude that:

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

Next, we can check the square of numbers between 4 and 5 to narrow it down further.

Let's try \( 4.4 \):

\[
4.4^2 = 19.36
\]

This means \( \sqrt{19} < 4.4 \).

Now, let's try \( 4.3 \):

\[
4.3^2 = 18.49
\]

This shows that \( 4.3 < \sqrt{19} \).

We can conclude that:

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

For a more precise approximation, we can try with another number, \( 4.35 \):

\[
4.35^2 = 18.9225
\]

Thus, \( 4.35 < \sqrt{19} \).

Now let's try \( 4.36 \):

\[
4.36^2 = 19.0496
\]

From this, we see that:

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

Therefore, the approximate value of \( \sqrt{19} \) is around \( 4.358 \). You can represent this on a number line just slightly above 4.35 but before 4.36.