What willl be the simplest form of `(sqrt(45)+sqrt(20))/(sqrt(5))`?

Options

A. `5sqrt(5)`
B. `5`
C. `2sqrt(5)`
D. `sqrt(5)`

Answer

To simplify the expression \((\sqrt{45} + \sqrt{20}) / \sqrt{5}\), we will follow these steps:

### Step 1: Simplify \(\sqrt{45}\) and \(\sqrt{20}\)

1. **Factor \(\sqrt{45}\)**:
\[ \sqrt{45} = \sqrt{9 \times 5} = \sqrt{9} \times \sqrt{5} = 3\sqrt{5} \]

2. **Factor \(\sqrt{20}\)**:
\[ \sqrt{20} = \sqrt{4 \times 5} = \sqrt{4} \times \sqrt{5} = 2\sqrt{5} \]

### Step 2: Substitute back into the expression

Now, substitute the simplified forms back into the original expression:
\[ \frac{\sqrt{45} + \sqrt{20}}{\sqrt{5}} = \frac{3\sqrt{5} + 2\sqrt{5}}{\sqrt{5}} \]

### Step 3: Combine the terms in the numerator

Combine the terms in the numerator:
\[ 3\sqrt{5} + 2\sqrt{5} = (3 + 2)\sqrt{5} = 5\sqrt{5} \]

### Step 4: Simplify the fraction

Now, substitute this back into the expression:
\[ \frac{5\sqrt{5}}{\sqrt{5}} \]

Since \(\sqrt{5}\) in the numerator and denominator cancels out:
\[ = 5 \]

### Final Answer

Thus, the simplest form of \(\frac{\sqrt{45} + \sqrt{20}}{\sqrt{5}}\) is:
\[ \boxed{5} \]