After rationalizing the denominator of `(7)/(3sqrt(3) - 2sqrt(2))`, we get the denominator as

Options

A. `13`
B. `19`
C. `5`
D. `35`

Explanation

To rationalize the denominator of the expression \( \frac{7}{3\sqrt{3} - 2\sqrt{2}} \), we follow these steps:

### Step 1: Identify the expression
We start with the expression:
\[ \frac{7}{3\sqrt{3} - 2\sqrt{2}} \]

### Step 2: Multiply by the conjugate
To rationalize the denominator, we multiply both the numerator and the denominator by the conjugate of the denominator. The conjugate of \( 3\sqrt{3} - 2\sqrt{2} \) is \( 3\sqrt{3} + 2\sqrt{2} \). Thus, we multiply:
\[ \frac{7}{3\sqrt{3} - 2\sqrt{2}} \cdot \frac{3\sqrt{3} + 2\sqrt{2}}{3\sqrt{3} + 2\sqrt{2}} \]

### Step 3: Apply the multiplication
Now, we perform the multiplication in the numerator and denominator:
- **Numerator**:
\[ 7 \cdot (3\sqrt{3} + 2\sqrt{2}) = 21\sqrt{3} + 14\sqrt{2} \]
- **Denominator**:
Using the identity \( (a - b)(a + b) = a^2 - b^2 \):
\[ (3\sqrt{3})^2 - (2\sqrt{2})^2 \]
Calculating each term:
\[ (3\sqrt{3})^2 = 9 \cdot 3 = 27 \]
\[ (2\sqrt{2})^2 = 4 \cdot 2 = 8 \]
Thus, the denominator becomes:
\[ 27 - 8 = 19 \]

### Step 4: Write the final expression
After rationalizing, we have:
\[ \frac{21\sqrt{3} + 14\sqrt{2}}{19} \]

### Conclusion
The denominator after rationalizing is:
\[ \boxed{19} \]

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