Find the square root of
`sqrt(27)+sqrt(15)`.

Answer

To find the square root of \( \sqrt{27} + \sqrt{15} \), we can follow these steps:

### Step 1: Simplify \( \sqrt{27} \) and \( \sqrt{15} \)

First, we simplify \( \sqrt{27} \) and \( \sqrt{15} \):

\[ \sqrt{27} = \sqrt{9 \times 3} = \sqrt{9} \cdot \sqrt{3} = 3\sqrt{3} \]

\[ \sqrt{15} = \sqrt{3 \times 5} = \sqrt{3} \cdot \sqrt{5} \]

### Step 2: Combine the square roots

Now, we can combine the two simplified terms:

\[ \sqrt{27} + \sqrt{15} = 3\sqrt{3} + \sqrt{15} \]

### Step 3: Find the square root of the sum

Next, we need to find the square root of the entire expression:

\[ \sqrt{3\sqrt{3} + \sqrt{15}} \]

### Step 4: Factor out common terms

To simplify further, we can factor out \( \sqrt{3} \):

\[ = \sqrt{\sqrt{3}(3 + \sqrt{5})} \]

### Step 5: Final simplification

Now, we can express the square root:

\[ = \sqrt{3} \cdot \sqrt{3 + \sqrt{5}} \]

Thus, the final answer is:

\[ \sqrt{27} + \sqrt{15} = \sqrt{3} \cdot \sqrt{3 + \sqrt{5}} \]