Find the square root of
`sqrt(32)-sqrt(24)`.

Answer

To find the square root of \( \sqrt{32} - \sqrt{24} \), we can follow these steps:

### Step 1: Simplify the square roots
First, we simplify \( \sqrt{32} \) and \( \sqrt{24} \).

\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \cdot \sqrt{2} = 4\sqrt{2} \]

\[ \sqrt{24} = \sqrt{4 \times 6} = \sqrt{4} \cdot \sqrt{6} = 2\sqrt{6} \]

### Step 2: Substitute back into the expression
Now we substitute these simplified forms back into the expression:

\[ \sqrt{32} - \sqrt{24} = 4\sqrt{2} - 2\sqrt{6} \]

### Step 3: Factor out the common term
Next, we can factor out a common term from the expression:

\[ = 2(2\sqrt{2} - \sqrt{6}) \]

### Step 4: Find the square root of the expression
Now we need to find the square root of \( 2(2\sqrt{2} - \sqrt{6}) \):

\[ \sqrt{2(2\sqrt{2} - \sqrt{6})} = \sqrt{2} \cdot \sqrt{2\sqrt{2} - \sqrt{6}} \]

### Step 5: Simplify further if possible
To simplify \( \sqrt{2\sqrt{2} - \sqrt{6}} \), we can express it in a different way:

Let \( x = \sqrt{2\sqrt{2} - \sqrt{6}} \).

To simplify, we can try to express \( 2\sqrt{2} - \sqrt{6} \) in a form that can be squared.

### Step 6: Rationalizing or completing the square
We can try to express \( 2\sqrt{2} - \sqrt{6} \) in terms of a perfect square.

Let’s assume:

\[ 2\sqrt{2} - \sqrt{6} = a - b \]

Squaring both sides gives:

\[ (2\sqrt{2} - \sqrt{6})^2 = a^2 - 2ab + b^2 \]

This might be complex, so we can directly compute \( 2\sqrt{2} - \sqrt{6} \) and check if it can be simplified further.

### Final Result
Thus, the final expression for the square root is:

\[ \sqrt{2} \cdot \sqrt{2\sqrt{2} - \sqrt{6}} \]