To find the approximate value of \(\sqrt{39}\) using a number line, we can identify two perfect squares between which 39 falls.
The perfect squares are:
- \(6^2 = 36\)
- \(7^2 = 49\)
This means that \(\sqrt{39}\) will be between 6 and 7. To get a more precise approximation, we can compare it to numbers like 6.1 and 6.2.
Calculating these:
- \(6.1^2 = 37.21\)
- \(6.2^2 = 38.44\)
- \(6.3^2 = 39.69\)
Thus, \(\sqrt{39}\) is between \(6.2\) and \(6.3\). Since \(39\) is closer to \(36\) than to \(49\), we can refine it further and estimate \(\sqrt{39} \approx 6.24\).
On a number line, you would place \(\sqrt{39}\) a little to the right of 6.2 and a little to the left of 6.3, approximately around 6.24.