Given `sqrt(2)=1.414`. The value of `sqrt(8)+2sqrt(32)-3sqrt(128)+4sqrt(50)` is

Options

A. A) `8.484`
B. B) `8.526`
C. C) `8.426`
D. D) `8.876`

Answer

To solve the expression \( \sqrt{8} + 2\sqrt{32} - 3\sqrt{128} + 4\sqrt{50} \) given that \( \sqrt{2} = 1.414 \), we will simplify each term step by step.

### Step 1: Simplify \( \sqrt{8} \)
\[ \sqrt{8} = \sqrt{4 \times 2} = \sqrt{4} \times \sqrt{2} = 2\sqrt{2} \]

### Step 2: Simplify \( 2\sqrt{32} \)
\[ \sqrt{32} = \sqrt{16 \times 2} = \sqrt{16} \times \sqrt{2} = 4\sqrt{2} \]
Thus,
\[ 2\sqrt{32} = 2 \times 4\sqrt{2} = 8\sqrt{2} \]

### Step 3: Simplify \( -3\sqrt{128} \)
\[ \sqrt{128} = \sqrt{64 \times 2} = \sqrt{64} \times \sqrt{2} = 8\sqrt{2} \]
Thus,
\[ -3\sqrt{128} = -3 \times 8\sqrt{2} = -24\sqrt{2} \]

### Step 4: Simplify \( 4\sqrt{50} \)
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]
Thus,
\[ 4\sqrt{50} = 4 \times 5\sqrt{2} = 20\sqrt{2} \]

### Step 5: Combine all the simplified terms
Now we can combine all the terms:
\[ \sqrt{8} + 2\sqrt{32} - 3\sqrt{128} + 4\sqrt{50} = 2\sqrt{2} + 8\sqrt{2} - 24\sqrt{2} + 20\sqrt{2} \]

Combine the coefficients of \( \sqrt{2} \):
\[ (2 + 8 - 24 + 20)\sqrt{2} = 6\sqrt{2} \]

### Step 6: Substitute \( \sqrt{2} \) with its value
Now, substitute \( \sqrt{2} = 1.414 \):
\[ 6\sqrt{2} = 6 \times 1.414 = 8.484 \]

### Final Answer
Thus, the value of \( \sqrt{8} + 2\sqrt{32} - 3\sqrt{128} + 4\sqrt{50} \) is \( \boxed{8.484} \).