Solve or simplify the following problem, using the properties of roots: `sqrt(63) + sqrt(28)`

Answer

To solve the expression \( \sqrt{63} + \sqrt{28} \) using the properties of roots, we can follow these steps:

### Step 1: Factor the numbers under the square roots
We start by breaking down \( \sqrt{63} \) and \( \sqrt{28} \) into their prime factors.

- \( 63 = 9 \times 7 \)
- \( 28 = 4 \times 7 \)

### Step 2: Rewrite the square roots
Using the properties of square roots, we can rewrite the expression:

\[ \sqrt{63} = \sqrt{9 \times 7} = \sqrt{9} \times \sqrt{7} \]
\[ \sqrt{28} = \sqrt{4 \times 7} = \sqrt{4} \times \sqrt{7} \]

### Step 3: Simplify the square roots
Now we simplify \( \sqrt{9} \) and \( \sqrt{4} \):

\[ \sqrt{9} = 3 \quad \text{and} \quad \sqrt{4} = 2 \]

### Step 4: Substitute back into the expression
Now we can substitute these values back into our expression:

\[ \sqrt{63} + \sqrt{28} = 3\sqrt{7} + 2\sqrt{7} \]

### Step 5: Combine like terms
Since both terms contain \( \sqrt{7} \), we can combine them:

\[ 3\sqrt{7} + 2\sqrt{7} = (3 + 2)\sqrt{7} = 5\sqrt{7} \]

### Final Answer
Thus, the simplified form of \( \sqrt{63} + \sqrt{28} \) is:

\[ \boxed{5\sqrt{7}} \]

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