Using a number line, what is the approximate value of 19−−√?
The approximate value of $\sqrt{19}$ can be found by finding the value between which two consecutive numbers on either side of 19 it lies. Since $4^2 = 16$ and $5^2 = 25$, we know that $4 < \sqrt{19} < 5$. Therefore, the approximate value of $\sqrt{19}$ is $\boxed{4.36}$.
To find the approximate value of √19 using a number line, we can start by locating the whole number value closest to the square root of 19.
The whole number value closest to √19 is 4.
To refine our estimation and get a more precise value, we can divide the interval between 4 and 5 on the number line into smaller increments.
Since there are 10 equally spaced divisions between 4 and 5, we can divide the interval into tenths.
Moving one-tenth of the way between 4 and 5 gives us a value of approximately 4.1.
We can continue this process to refine our estimation even further.
Moving another tenth of the way gives us approximately 4.2.
Continuing this process, we can estimate that √19 is approximately 4.3 on the number line.