Evaluate : `(sqrt(24)+sqrt(6))/(sqrt(24)-sqrt(6))`

Options

A. `2`
B. `3`
C. `4`
D. `5`

Answer

To evaluate the expression \((\sqrt{24} + \sqrt{6}) / (\sqrt{24} - \sqrt{6})\), we can follow these steps:

### Step 1: Simplify \(\sqrt{24}\)
First, we simplify \(\sqrt{24}\):
\[ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \times \sqrt{6} = 2\sqrt{6} \]

### Step 2: Substitute \(\sqrt{24}\) in the expression
Now, substitute \(2\sqrt{6}\) for \(\sqrt{24}\) in the original expression:
\[ \frac{\sqrt{24} + \sqrt{6}}{\sqrt{24} - \sqrt{6}} = \frac{2\sqrt{6} + \sqrt{6}}{2\sqrt{6} - \sqrt{6}} \]

### Step 3: Combine like terms
Combine the terms in the numerator and the denominator:
\[ = \frac{(2\sqrt{6} + \sqrt{6})}{(2\sqrt{6} - \sqrt{6})} = \frac{3\sqrt{6}}{\sqrt{6}} \]

### Step 4: Simplify the fraction
Now, simplify the fraction:
\[ = 3 \]

### Final Answer
Thus, the value of the expression \((\sqrt{24} + \sqrt{6}) / (\sqrt{24} - \sqrt{6})\) is:
\[ \boxed{3} \]

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