Write the least ( smallest ) rationlising factor of :
` sqrt((2)/(3))`

Answer

To find the least (smallest) rationalizing factor of \( \sqrt{\frac{2}{3}} \), we will follow these steps:

### Step 1: Rewrite the expression
We start with the expression \( \sqrt{\frac{2}{3}} \). This can be rewritten as:
\[ \sqrt{\frac{2}{3}} = \frac{\sqrt{2}}{\sqrt{3}} \]

### Step 2: Identify the rationalizing factor
To rationalize the denominator (which is \( \sqrt{3} \)), we need to multiply both the numerator and the denominator by \( \sqrt{3} \). This will help eliminate the square root in the denominator.

### Step 3: Multiply by the rationalizing factor
Multiply the expression by \( \frac{\sqrt{3}}{\sqrt{3}} \):
\[ \frac{\sqrt{2}}{\sqrt{3}} \cdot \frac{\sqrt{3}}{\sqrt{3}} = \frac{\sqrt{2} \cdot \sqrt{3}}{3} = \frac{\sqrt{6}}{3} \]

### Step 4: Determine the smallest rationalizing factor
The smallest rationalizing factor that we used to rationalize \( \sqrt{\frac{2}{3}} \) is \( \sqrt{3} \). However, since we are looking for the least rationalizing factor of the original expression \( \sqrt{\frac{2}{3}} \), we can express it as:
\[ \text{Smallest rationalizing factor} = \sqrt{\frac{2}{3}} \]

Thus, the smallest rationalizing factor of \( \sqrt{\frac{2}{3}} \) is \( \sqrt{\frac{2}{3}} \) itself.

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

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