Which two consecutive whole numbers does StartRoot 39 EndRoot lie between? Why?

Question

5 and 6 because 39 falls between 52 = 25 and 62 = 36.
4 and 6 because 39 falls between 42 = 16 and 62 = 36.
6 and 7 because 39 falls between 62 = 36 and 72 = 49.
5 and 7 because 39 falls between 52 = 25 and 72 = 49.

Answer 1

To determine which two consecutive whole numbers \(\sqrt{39}\) lies between, we need to find the perfect squares that are closest to 39.

1. \(5^2 = 25\)
2. \(6^2 = 36\)
3. \(7^2 = 49\)

Now we observe that:

• \(36 < 39 < 49\)

This indicates that \(\sqrt{39}\) lies between \(6\) (since \(\sqrt{36} = 6\)) and \(7\) (since \(\sqrt{49} = 7\)).

Thus, the correct answer is that \(\sqrt{39}\) lies between 6 and 7 because \(39\) falls between \(6^2 = 36\) and \(7^2 = 49\).