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

Answer

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

### Step 1: Simplify \( \sqrt{12} \)
First, we need to express \( \sqrt{12} \) in its simplest form. We can factor 12 into its prime factors:
\[ 12 = 4 \times 3 = 2^2 \times 3 \]
Now, we can write:
\[ \sqrt{12} = \sqrt{4 \times 3} = \sqrt{4} \times \sqrt{3} = 2\sqrt{3} \]

### Step 2: Identify the Rationalizing Factor
To rationalize \( \sqrt{12} \), we need to eliminate the square root in the denominator. The rationalizing factor is the number that, when multiplied with \( \sqrt{12} \), will give a rational number. Since we simplified \( \sqrt{12} \) to \( 2\sqrt{3} \), we need to multiply by \( \sqrt{3} \) to rationalize it:
\[ \text{Rationalizing factor} = \sqrt{3} \]

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