Find the value of `5/(6sqrt(6)) xx (12sqrt(30))/(25sqrt(5))`.

Answer

To solve the expression \( \frac{5}{6\sqrt{6}} \times \frac{12\sqrt{30}}{25\sqrt{5}} \), we will follow these steps:

### Step 1: Write the expression clearly
We start with the expression:
\[ \frac{5}{6\sqrt{6}} \times \frac{12\sqrt{30}}{25\sqrt{5}} \]

### Step 2: Multiply the fractions
When multiplying fractions, we multiply the numerators together and the denominators together:
\[ \frac{5 \times 12\sqrt{30}}{6\sqrt{6} \times 25\sqrt{5}} \]

### Step 3: Simplify the numerator and denominator
Calculating the numerator:
\[ 5 \times 12\sqrt{30} = 60\sqrt{30} \]
Calculating the denominator:
\[ 6 \times 25\sqrt{6} \times \sqrt{5} = 150\sqrt{30} \]
So, we have:
\[ \frac{60\sqrt{30}}{150\sqrt{30}} \]

### Step 4: Cancel out common terms
Since \(\sqrt{30}\) is present in both the numerator and the denominator, we can cancel it out:
\[ \frac{60}{150} \]

### Step 5: Simplify the fraction
Now, we simplify \(\frac{60}{150}\):
\[ \frac{60 \div 30}{150 \div 30} = \frac{2}{5} \]

### Final Answer
Thus, the value of the expression is:
\[ \frac{2}{5} \]