Evaluate '|[sqrt(6), sqrt(5)], [sqrt(20), sqrt(24)]|`

Explanation

To evaluate the determinant of the given matrix \(\begin{bmatrix} \sqrt{6} & \sqrt{5} \\ \sqrt{20} & \sqrt{24} \end{bmatrix}\), we can follow these steps:

### Step 1: Write down the determinant formula
The determinant of a \(2 \times 2\) matrix \(\begin{bmatrix} a & b \\ c & d \end{bmatrix}\) is given by the formula:
\[ \text{det} = ad - bc \]
In our case, we have:
- \(a = \sqrt{6}\)
- \(b = \sqrt{5}\)
- \(c = \sqrt{20}\)
- \(d = \sqrt{24}\)

### Step 2: Substitute the values into the formula
Now, substituting the values into the determinant formula:
\[ \text{det} = (\sqrt{6})(\sqrt{24}) - (\sqrt{5})(\sqrt{20}) \]

### Step 3: Simplify the terms
We can simplify the terms:
- \(\sqrt{6} \cdot \sqrt{24} = \sqrt{6 \cdot 24} = \sqrt{144} = 12\)
- \(\sqrt{5} \cdot \sqrt{20} = \sqrt{5 \cdot 20} = \sqrt{100} = 10\)

### Step 4: Calculate the determinant
Now substituting back into the determinant:
\[ \text{det} = 12 - 10 = 2 \]

### Final Result
Thus, the value of the determinant is:
\[ \boxed{2} \]