Solution:

To find the value of (√x-1/x), we first need to calculate the value of x, which is given as X = 3 √8.

Step 1: Calculate the value of √8:
√8 = √(2*2*2) = 2√2

Step 2: Substitute the value of √8 in X:
X = 3 * 2√2 = 6√2

Now, we can substitute the value of X in (√x-1/x) and simplify the expression.

Step 3: Substitute the value of X in the expression (√x-1/x):
(√x-1/x) = (√6√2 - 1/6√2)

Step 4: Rationalize the denominator:
To rationalize the denominator, we multiply both the numerator and denominator by the conjugate of the denominator, which is (√6√2 + 1/6√2).

(√x-1/x) = (√6√2 - 1/6√2) * (√6√2 + 1/6√2) / (√6√2 + 1/6√2)

Step 5: Simplify the expression after multiplying:
(√6√2 - 1/6√2) * (√6√2 + 1/6√2) = (6√2 - 1) / (36 * 2)

Step 6: Simplify the expression further:
(6√2 - 1) / (36 * 2) = (6√2 - 1) / 72

Therefore, the value of (√x-1/x) is (6√2 - 1) / 72.

Final Answer: (√x-1/x) = (6√2 - 1) / 72