To approximate the square root of 19 (√19) on a number line, we can look for two perfect squares between which 19 lies.
The perfect squares near 19 are:
- \(4^2 = 16\)
- \(5^2 = 25\)
Since \(16 < 19 < 25\), we know that \(4 < \sqrt{19} < 5\).
To get a more specific approximation, we can test some numbers between 4 and 5:
- \(4.3^2 = 18.49\) (which is slightly less than 19)
- \(4.4^2 = 19.36\) (which is slightly more than 19)
So, we find that \(4.3 < \sqrt{19} < 4.4\).
Now we can examine the answer choices more closely:
- 4.25
- 4.38
- 4.5
- 4.13
Among these, 4.38 is closer to the approximate root found above. Thus, the best choice is:
4.38