The value of `sqrt(18) + sqrt(50) - sqrt(32)` is

Options

A. `4sqrt2`
B. `3sqrt2`
C. `2sqrt2`
D. `sqrt2`

Answer

To solve the expression \( \sqrt{18} + \sqrt{50} - \sqrt{32} \), we will simplify each square root individually and then combine the results.

### Step-by-Step Solution:

1. **Simplify \( \sqrt{18} \)**:
\[ \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \times \sqrt{2} = 3\sqrt{2} \]

2. **Simplify \( \sqrt{50} \)**:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

3. **Simplify \( \sqrt{32} \)**:
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]

4. **Combine the results**:
Now we can substitute the simplified forms back into the original expression:
\[ \sqrt{18} + \sqrt{50} - \sqrt{32} = 3\sqrt{2} + 5\sqrt{2} - 4\sqrt{2} \]

5. **Combine like terms**:
\[ (3 + 5 - 4)\sqrt{2} = 4\sqrt{2} \]

Thus, the value of \( \sqrt{18} + \sqrt{50} - \sqrt{32} \) is \( 4\sqrt{2} \).

### Final Answer:
\[ \text{The value is } 4\sqrt{2}. \]