Question

Using a number line,what is the approximate value of square root 19?
A.4.25
B.4.5
C.4.38
D.4.13

Answer 1

To approximate the value of \(\sqrt{19}\) using a number line, we can first identify the squares of whole numbers around 19.

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

Since \(19\) is between \(16\) and \(25\), we know that:

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

Next, we can check some decimal values between \(4\) and \(5\):

- \(4.25^2 = 18.0625\)
- \(4.5^2 = 20.25\)
- \(4.4^2 = 19.36\)
- \(4.38^2 \approx 19.0244\)
- \(4.3^2 = 18.49\)

From these calculations, we can see that:

- \(4.38^2\) is a close approximation, being just above \(19\).
- \(4.4^2\) is above \(19\), while \(4.3^2\) is below \(19\).

Given these estimates, the best choice among the options provided is \(C. 4.38\), as it gives a value very close to \(\sqrt{19}\).

Thus, the approximate value of \(\sqrt{19}\) is:

**C. 4.38**