We can simplify the square roots:
√2 = √(2 × 1) = √2 × √1
√18 = √(9 × 2) = √9 × √2 = 3√2
√50 = √(25 × 2) = √25 × √2 = 5√2
Now we can find the mean:
(mean) = (sum of numbers) / (number of numbers)
(mean) = (√2 + 3√2 + 5√2) / 3
(mean) = (9√2) / 3
(mean) = 3√2
Therefore, the mean of the numbers √2, √18, and √50 is 3√2.