Write the lowest rationalising factor of :
`sqrt(5) -sqrt(2)`

Answer

To find the lowest rationalizing factor of \( \sqrt{5} - \sqrt{2} \), we will follow these steps:

### Step 1: Identify the expression
We start with the expression \( \sqrt{5} - \sqrt{2} \).

### Step 2: Determine the conjugate
The rationalizing factor is typically the conjugate of the given expression. The conjugate of \( \sqrt{5} - \sqrt{2} \) is obtained by changing the sign between the two terms. Therefore, the conjugate is \( \sqrt{5} + \sqrt{2} \).

### Step 3: Write the lowest rationalizing factor
Thus, the lowest rationalizing factor of \( \sqrt{5} - \sqrt{2} \) is:
\[ \sqrt{5} + \sqrt{2} \]

### Step 4: Verification (optional)
To verify that this is indeed a rationalizing factor, we can multiply the original expression by its conjugate:
\[ (\sqrt{5} - \sqrt{2})(\sqrt{5} + \sqrt{2}) = \sqrt{5}^2 - \sqrt{2}^2 = 5 - 2 = 3 \]
Since 3 is a rational number, this confirms that \( \sqrt{5} + \sqrt{2} \) is the correct rationalizing factor.

### Final Answer
The lowest rationalizing factor of \( \sqrt{5} - \sqrt{2} \) is \( \sqrt{5} + \sqrt{2} \).

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