Find the simplest value of `2sqrt(50)+sqrt(18)-sqrt(72)` (given `sqrt(2)=1.414` ) .

Options

A. `4.242`
B. `9.898`
C. `10.312`
D. `8.484`

Answer

To simplify the expression \(2\sqrt{50} + \sqrt{18} - \sqrt{72}\), we can follow these steps:

### Step 1: Simplify each square root term
1. **Simplify \(\sqrt{50}\)**:
\[ \sqrt{50} = \sqrt{25 \times 2} = \sqrt{25} \times \sqrt{2} = 5\sqrt{2} \]
Therefore, \(2\sqrt{50} = 2 \times 5\sqrt{2} = 10\sqrt{2}\).

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

3. **Simplify \(\sqrt{72}\)**:
\[ \sqrt{72} = \sqrt{36 \times 2} = \sqrt{36} \times \sqrt{2} = 6\sqrt{2} \]

### Step 2: Substitute the simplified terms back into the expression
Now substituting the simplified terms back into the original expression:
\[ 2\sqrt{50} + \sqrt{18} - \sqrt{72} = 10\sqrt{2} + 3\sqrt{2} - 6\sqrt{2} \]

### Step 3: Combine like terms
Combine the coefficients of \(\sqrt{2}\):
\[ 10\sqrt{2} + 3\sqrt{2} - 6\sqrt{2} = (10 + 3 - 6)\sqrt{2} = 7\sqrt{2} \]

### Step 4: Substitute the value of \(\sqrt{2}\)
Given that \(\sqrt{2} = 1.414\), we can now calculate:
\[ 7\sqrt{2} = 7 \times 1.414 = 9.898 \]

### Final Answer
Thus, the simplest value of \(2\sqrt{50} + \sqrt{18} - \sqrt{72}\) is approximately \(9.898\).

---