The rationalising factor of `3sqrt(3)` is

Options

A. `(1)/(3)`
B. `3`
C. `-3`
D. `sqrt(3)`

Answer

To find the rationalizing factor of \(3\sqrt{3}\), we need to determine a number that, when multiplied by \(3\sqrt{3}\), results in a rational number.

### Step-by-step Solution:

1. **Identify the irrational number**: The given expression is \(3\sqrt{3}\). This is an irrational number because it contains the square root of a non-perfect square.

2. **Determine the rationalizing factor**: To rationalize \(3\sqrt{3}\), we need to multiply it by another expression that will eliminate the square root. The simplest way to do this is to multiply by \(\sqrt{3}\).

3. **Multiply the expression**:
\[ 3\sqrt{3} \times \sqrt{3} = 3 \times (\sqrt{3} \times \sqrt{3}) = 3 \times 3 = 9 \]
Here, we used the property that \(\sqrt{a} \times \sqrt{a} = a\).

4. **Conclusion**: The result of the multiplication is \(9\), which is a rational number. Therefore, the rationalizing factor of \(3\sqrt{3}\) is \(\sqrt{3}\).

### Final Answer:
The rationalizing factor of \(3\sqrt{3}\) is \(\sqrt{3}\).

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