The value of `sqrt32 - sqrt128 + sqrt50` correct to 3 places of decimals is :

Options

A. 1.732
B. 1.141
C. 1.414
D. 1.441

Answer

To solve the expression \( \sqrt{32} - \sqrt{128} + \sqrt{50} \) and find its value correct to three decimal places, we can follow these steps:

### Step 1: Simplify each square root
We start by simplifying each square root in the expression.

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

2. **For \( \sqrt{128} \)**:
\[ \sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2} \]

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

### Step 2: Substitute back into the expression
Now we can substitute these simplified forms back into the original expression:
\[ \sqrt{32} - \sqrt{128} + \sqrt{50} = 4\sqrt{2} - 8\sqrt{2} + 5\sqrt{2} \]

### Step 3: Combine like terms
Next, we combine the terms:
\[ (4\sqrt{2} - 8\sqrt{2} + 5\sqrt{2}) = (4 - 8 + 5)\sqrt{2} = 1\sqrt{2} = \sqrt{2} \]

### Step 4: Calculate the numerical value of \( \sqrt{2} \)
Now we need to find the numerical value of \( \sqrt{2} \):
\[ \sqrt{2} \approx 1.414 \]

### Step 5: Round to three decimal places
Finally, we round \( 1.414 \) to three decimal places:
\[ \sqrt{2} \approx 1.414 \]

Thus, the value of \( \sqrt{32} - \sqrt{128} + \sqrt{50} \) correct to three decimal places is:
\[ \boxed{1.414} \]