If 25x8913 is divisible by 3, where x is single digit odd number and y – x = 1, then find the value of √(2xy).

Step 1: The rule of divisibility by 3 states that a number is divisible by 3 if the sum of its digits is divisible by 3.

Step 2: In the given number 25x8913, we need to find the value of 'x' such that the number becomes divisible by 3.

Step 3: Add the digits of the number, excluding 'x' (2 + 5 + 8 + 9 + 1 + 3 = 28).

Step 4: Now, we need to find a single digit odd number 'x' which when added to 28, the sum should be divisible by 3. The possible single digit odd numbers are 1, 3, 5, 7, 9.

Step 5: By trying these numbers, we find that 'x' = 1 makes the sum 29 which is not divisible by 3, 'x' = 3 makes the sum 31 which is not divisible by 3, 'x' = 5 makes the sum 33 which is divisible by 3. So, 'x' = 5.

Step 6: Now, we know that y - x = 1. Substituting 'x' = 5, we get 'y' = 6.

Step 7: Finally, we need to find the value of √(2xy). Substituting 'x' = 5 and 'y' = 6, we get √(256) = √60.

So, the value of √(2xy) is √60.