Step 1: Understanding the Question:
The root mean square (r.m.s.) speed is defined as the square root of the average of the squares of the speeds of all individual molecules.
Step 2: Key Formula or Approach:
\[ v_{rms} = \sqrt{\frac{v_1^2 + v_2^2 + ... + v_n^2}{n}} \]
Step 3: Detailed Explanation:
Given speeds: 2, 5, 3, 6, 3, 5 m/s. Number of molecules $n = 6$.
Square the speeds: $4, 25, 9, 36, 9, 25$.
Sum of squares:
\[ \sum v^2 = 4 + 25 + 9 + 36 + 9 + 25 = 108 \]
Mean of squares:
\[ \overline{v^2} = \frac{108}{6} = 18 \]
Root Mean Square:
\[ v_{rms} = \sqrt{18} = \sqrt{9 \times 2} = 3\sqrt{2} \]
Substituting $\sqrt{2} \approx 1.414$:
\[ v_{rms} = 3 \times 1.414 = 4.242 \text{ m/s} \]
Step 4: Final Answer:
The r.m.s. speed is approximately 4.24 m/s.