Write the least ( smallest ) rationlising factor of :
` 2 sqrt(12)`

Answer

To find the least (smallest) rationalizing factor of \( 2 \sqrt{12} \), we will follow these steps:

### Step 1: Simplify \( \sqrt{12} \)
We start by simplifying \( \sqrt{12} \):
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]
So, we can rewrite \( 2\sqrt{12} \) as:
\[ 2\sqrt{12} = 2 \times 2\sqrt{3} = 4\sqrt{3} \]

### Step 2: Identify the irrational part
Now, we have \( 4\sqrt{3} \). The irrational part here is \( \sqrt{3} \).

### Step 3: Find the rationalizing factor
To rationalize \( \sqrt{3} \), we need to multiply it by itself:
\[ \text{Rationalizing factor} = \sqrt{3} \times \sqrt{3} = 3 \]
This means that multiplying \( 4\sqrt{3} \) by \( \sqrt{3} \) will give us a rational number.

### Step 4: State the smallest rationalizing factor
Thus, the smallest rationalizing factor of \( 2\sqrt{12} \) is:
\[ \sqrt{3} \]

### Final Answer
The least (smallest) rationalizing factor of \( 2\sqrt{12} \) is \( \sqrt{3} \).

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