Write the lowest rationalising factor of :
`15 -3sqrt(2)`

Answer

To find the lowest rationalizing factor of the expression \( 15 - 3\sqrt{2} \), we can follow these steps:

### Step 1: Identify the Rationalizing Factor
The rationalizing factor of a binomial expression of the form \( a - b \) is its conjugate, which is \( a + b \). In this case, we have:
- \( a = 15 \)
- \( b = 3\sqrt{2} \)

Thus, the conjugate (or rationalizing factor) of \( 15 - 3\sqrt{2} \) is:
\[ 15 + 3\sqrt{2} \]

### Step 2: Multiply the Expression by its Rationalizing Factor
To rationalize \( 15 - 3\sqrt{2} \), we multiply it by its conjugate:
\[ (15 - 3\sqrt{2})(15 + 3\sqrt{2}) \]

### Step 3: Apply the Difference of Squares Formula
Using the difference of squares formula \( (a - b)(a + b) = a^2 - b^2 \), we can simplify the expression:
\[ = 15^2 - (3\sqrt{2})^2 \]

### Step 4: Calculate the Squares
Now, we calculate each square:
- \( 15^2 = 225 \)
- \( (3\sqrt{2})^2 = 3^2 \cdot (\sqrt{2})^2 = 9 \cdot 2 = 18 \)

### Step 5: Subtract the Results
Now, we subtract the results:
\[ 225 - 18 = 207 \]

### Conclusion
Thus, the lowest rationalizing factor of \( 15 - 3\sqrt{2} \) is:
\[ \boxed{15 + 3\sqrt{2}} \]