Solution:

The root mean square (r.m.s.) speed \( v_{\text{rms}} \) for \( n \) molecules with speeds \( v_1, v_2, \ldots, v_n \) is calculated by:

\[
v_{\text{rms}} = \sqrt{\frac{v_1^2 + v_2^2 + v_3^2 + \cdots + v_n^2}{n}}
\]

Given speeds are: \( 2, 3, 4, 5, 6 \).

1. Calculate the squares:
\[
2^2 = 4, \quad 3^2 = 9, \quad 4^2 = 16, \quad 5^2 = 25, \quad 6^2 = 36
\]

2. Sum of the squares:
\[
4 + 9 + 16 + 25 + 36 = 90
\]

3. Divide by the number of molecules (5) and take the square root:
\[
v_{\text{rms}} = \sqrt{\frac{90}{5}} = \sqrt{18} \approx 4.24
\]

Thus, the r.m.s. speed is approximately \( 4.24 \).