Write the simplest rationalizing factor of `sqrt(27)`

Answer

To find the simplest rationalizing factor of \(\sqrt{27}\), we can follow these steps:

### Step 1: Simplify \(\sqrt{27}\)
We start by simplifying \(\sqrt{27}\). The number 27 can be expressed as a product of its prime factors:
\[ 27 = 3^3 \]
Now, we can write:
\[ \sqrt{27} = \sqrt{3^3} \]

### Step 2: Apply the property of square roots
Using the property of square roots, we can separate the factors:
\[ \sqrt{27} = \sqrt{3^2 \cdot 3} = \sqrt{3^2} \cdot \sqrt{3} \]
Since \(\sqrt{3^2} = 3\), we have:
\[ \sqrt{27} = 3\sqrt{3} \]

### Step 3: Identify the rationalizing factor
The rationalizing factor is essentially what we need to multiply \(\sqrt{27}\) by to eliminate the square root in the denominator. In this case, since we have \(\sqrt{3}\) as part of our simplified expression, the simplest rationalizing factor of \(\sqrt{27}\) is:
\[ \sqrt{3} \]

### Final Answer
Thus, the simplest rationalizing factor of \(\sqrt{27}\) is:
\[ \sqrt{3} \]

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