Find the value of `sqrt(32)-sqrt(128)+sqrt(50)` upto three places of decimal (correct value)

Options

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

Answer

To solve the expression \( \sqrt{32} - \sqrt{128} + \sqrt{50} \) up to three decimal places, we will simplify each square root term step by step.

### Step 1: Simplify \( \sqrt{32} \)

1. **Factor 32**:
\[ 32 = 16 \times 2 \]
2. **Take the square root**:
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]

### Step 2: Simplify \( \sqrt{128} \)

1. **Factor 128**:
\[ 128 = 64 \times 2 \]
2. **Take the square root**:
\[ \sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2} \]

### Step 3: Simplify \( \sqrt{50} \)

1. **Factor 50**:
\[ 50 = 25 \times 2 \]
2. **Take the square root**:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]

### Step 4: Substitute back into the expression

Now we substitute the simplified terms back into the original expression:
\[ \sqrt{32} - \sqrt{128} + \sqrt{50} = 4\sqrt{2} - 8\sqrt{2} + 5\sqrt{2} \]

### Step 5: Combine like terms

Combine the coefficients of \( \sqrt{2} \):
\[ (4 - 8 + 5)\sqrt{2} = 1\sqrt{2} = \sqrt{2} \]

### Step 6: Calculate the numerical value of \( \sqrt{2} \)

Using the known value:
\[ \sqrt{2} \approx 1.414 \]

### Final Answer

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