Find the square root of
`sqrt(18)-sqrt(16)`.

Answer

To find the square root of \( \sqrt{18} - \sqrt{16} \), we will follow these steps:

### Step 1: Simplify the square roots
We start with the expression:
\[ \sqrt{18} - \sqrt{16} \]
We know that:
\[ \sqrt{16} = 4 \]
Now, we simplify \( \sqrt{18} \):
\[ \sqrt{18} = \sqrt{9 \cdot 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \]
So, we can rewrite the expression as:
\[ 3\sqrt{2} - 4 \]

### Step 2: Rewrite the expression
Now we have:
\[ \sqrt{18} - \sqrt{16} = 3\sqrt{2} - 4 \]
We will denote this entire expression as \( n \):
\[ n = 3\sqrt{2} - 4 \]

### Step 3: Factor out the common term
Next, we can factor out \( \sqrt{2} \) from the expression:
\[ n = \sqrt{2}(3 - 2\sqrt{2}) \]

### Step 4: Find the square root
Now we need to find the square root of \( n \):
\[ \sqrt{n} = \sqrt{\sqrt{2}(3 - 2\sqrt{2})} \]
This can be expressed as:
\[ \sqrt{n} = \sqrt{2}^{1/2} \cdot \sqrt{3 - 2\sqrt{2}} \]
Since \( \sqrt{2}^{1/2} = 2^{1/4} \), we have:
\[ \sqrt{n} = 2^{1/4} \cdot \sqrt{3 - 2\sqrt{2}} \]

### Step 5: Simplify \( \sqrt{3 - 2\sqrt{2}} \)
To simplify \( \sqrt{3 - 2\sqrt{2}} \), we can use the identity \( a - b = (a - b)^2 \):
\[ 3 - 2\sqrt{2} = (\sqrt{2} - 1)^2 \]
Thus:
\[ \sqrt{3 - 2\sqrt{2}} = \sqrt{(\sqrt{2} - 1)^2} = \sqrt{2} - 1 \]

### Final Answer
Now substituting back, we get:
\[ \sqrt{n} = 2^{1/4} \cdot (\sqrt{2} - 1) \]

### Summary
The square root of \( \sqrt{18} - \sqrt{16} \) is:
\[ \sqrt{n} = 2^{1/4}(\sqrt{2} - 1) \]