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

Question

Responses

4.25
4.25

4.38
4.38

4.5
4.5

4.13
4.13

Answer 1

To find the approximate value of \(\sqrt{19}\) using a number line, we can estimate its position between two perfect squares.

Since \(4^2 = 16\) and \(5^2 = 25\), we know that:

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

Next, we can find the decimals by squaring numbers between 4 and 5:

• \(4.4^2 = 19.36\) (too high)
• \(4.3^2 = 18.49\) (too low)
• \(4.35^2 = 18.9225\) (too low)
• \(4.36^2 = 19.0496\) (too high)

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

This suggests that the approximate value of \(\sqrt{19}\) lies closer to \(4.36\) or slightly above it, and definitely below \(4.4\).

Thus, the closest answer from your options is:

4.38