Simplify `sqrt""50+ sqrt""18- sqrt""8`
A. `8 sqrt2`
B. `7 sqrt2`
C. `6 sqrt2`
D. `5 sqrt""2`

Options

A. A
B. C
C. D
D. B

Answer

To simplify the expression \( \sqrt{50} + \sqrt{18} - \sqrt{8} \), we will follow these steps:

### Step 1: Simplify each square root term
1. **Simplify \( \sqrt{50} \)**:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

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

3. **Simplify \( \sqrt{8} \)**:
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \]

### Step 2: Substitute the simplified terms back into the expression
Now, we can substitute these simplified terms back into the original expression:
\[ \sqrt{50} + \sqrt{18} - \sqrt{8} = 5\sqrt{2} + 3\sqrt{2} - 2\sqrt{2} \]

### Step 3: Combine like terms
Combine the coefficients of \( \sqrt{2} \):
\[ (5 + 3 - 2)\sqrt{2} = 6\sqrt{2} \]

### Final Answer
Thus, the simplified expression is:
\[ \boxed{6\sqrt{2}} \]