Write the least ( smallest ) rationlising factor of :
` sqrt(18)`

Answer

To find the least rationalizing factor of \( \sqrt{18} \), we can follow these steps:

### Step 1: Simplify \( \sqrt{18} \)
We start by breaking down \( \sqrt{18} \) into its prime factors:
\[ \sqrt{18} = \sqrt{9 \times 2} \]

### Step 2: Take the square root of the perfect square
Next, we can simplify \( \sqrt{9} \):
\[ \sqrt{18} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

### Step 3: Identify the irrational part
In the expression \( 3\sqrt{2} \), the irrational part is \( \sqrt{2} \).

### Step 4: Find the rationalizing factor
To rationalize \( \sqrt{2} \), we multiply it by itself, which is \( \sqrt{2} \):
\[ \sqrt{2} \times \sqrt{2} = 2 \]
This means that \( \sqrt{2} \) is the rationalizing factor we need to convert \( 3\sqrt{2} \) into a rational number.

### Step 5: Conclusion
The least rationalizing factor of \( \sqrt{18} \) is:
\[ \sqrt{2} \]

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