To approximate the value of \(\sqrt{19}\), we can consider the perfect squares around 19.
We know that:
- \(\sqrt{16} = 4\)
- \(\sqrt{25} = 5\)
Since \(19\) is between \(16\) and \(25\), we know that \(\sqrt{19}\) is between \(4\) and \(5\).
To narrow it down:
- Calculating \(4.3^2 = 18.49\) (which is less than 19)
- Calculating \(4.4^2 = 19.36\) (which is greater than 19)
Therefore, \(\sqrt{19}\) is between \(4.3\) and \(4.4\).
This means 4.3 is a good approximation, and since it's the closest option given:
The approximate value of \(\sqrt{19}\) is 4.3.