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

Options

A. 1
B. 5
C. 19
D. 35

Answer

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

### Step 1: Identify the expression
The given expression is:
\[ \frac{3 \sqrt{2}}{3 \sqrt{2} - 2 \sqrt{2}} \]

### Step 2: Simplify the denominator
First, simplify the denominator:
\[ 3 \sqrt{2} - 2 \sqrt{2} = (3 - 2) \sqrt{2} = 1 \sqrt{2} = \sqrt{2} \]
So the expression becomes:
\[ \frac{3 \sqrt{2}}{\sqrt{2}} \]

### Step 3: Rationalize the denominator
To rationalize the denominator, we multiply both the numerator and the denominator by \(\sqrt{2}\):
\[ \frac{3 \sqrt{2}}{\sqrt{2}} \cdot \frac{\sqrt{2}}{\sqrt{2}} = \frac{3 \cdot 2}{2} = \frac{6}{2} = 3 \]

### Step 4: Identify the new denominator
After rationalizing, the denominator simplifies to:
\[ \sqrt{2} \cdot \sqrt{2} = 2 \]
However, since we have simplified the fraction to \(3\), we can conclude that the denominator is effectively \(1\) when expressed in the simplest form.

### Final Answer
The denominator after rationalizing is:
\[ 1 \]

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