using a number line, what is the approximate value of 39−−√ ?(1 point)

1 answer

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.