Question

Using a number line, what is the approximate value of 19−−√ 4.38 4.38 4.5 4.5 4.25 4.25 4.13

Answer 1

To approximate the value of \( \sqrt{19} \) using a number line, we first need to determine the approximate value of \( \sqrt{19} \) by comparing it with perfect squares.

1. Find perfect squares close to 19:
- \( 4^2 = 16 \)
- \( 5^2 = 25 \)

Since \( \sqrt{19} \) is between \( 4 \) and \( 5 \), we know that:
\[ 4 < \sqrt{19} < 5 \]

2. Next, we'll narrow it down to get closer:
- \( 4.25^2 = 18.0625 \)
- \( 4.5^2 = 20.25 \)

Since \( 18.0625 < 19 < 20.25 \), we conclude that:
\[ 4.25 < \sqrt{19} < 4.5 \]

3. We can try \( 4.35 \):
- \( 4.35^2 = 18.9225 \)

This is still less than 19, so:
\[ 4.35 < \sqrt{19} < 4.5 \]

4. Try \( 4.4 \):
- \( 4.4^2 = 19.36 \)

Since \( 19.36 > 19 \), we adjust to:
\[ 4.35 < \sqrt{19} < 4.4 \]

Finally, we can estimate \( \sqrt{19} \) to be around \( 4.36 \).

Thus, on a number line, we can place \( \sqrt{19} \) approximately at about \( 4.36 \) which is slightly closer to \( 4.4 \) but just below it.

So, the closest numbers on your number line are:
- \( 4.38 \)
- \( 4.25 \)
- \( 4.5 \)
- \( 4.13 \)

The approximation of \( \sqrt{19} \) is closest to \( 4.38 \).