Expressed in simplest form, `2sqrt(-50)-3sqrt(-8)` is

Options

A. `16isqrt(2)`
B. `3isqrt(2)`
C. `4isqrt(2)`
D. `-isqrt(2)`

Answer

To simplify the expression \(2\sqrt{-50} - 3\sqrt{-8}\), we will follow these steps:

### Step 1: Simplify \(2\sqrt{-50}\)

1. Recognize that \(\sqrt{-50}\) can be expressed as \(\sqrt{-1} \cdot \sqrt{50}\).
2. Since \(\sqrt{-1} = i\), we have:
\[ \sqrt{-50} = i\sqrt{50} \]
3. Now, simplify \(\sqrt{50}\):
\[ \sqrt{50} = \sqrt{25 \cdot 2} = \sqrt{25} \cdot \sqrt{2} = 5\sqrt{2} \]
4. Therefore, we can rewrite \(2\sqrt{-50}\) as:
\[ 2\sqrt{-50} = 2(i \cdot 5\sqrt{2}) = 10i\sqrt{2} \]

### Step 2: Simplify \(-3\sqrt{-8}\)

1. Similarly, \(\sqrt{-8}\) can be expressed as \(\sqrt{-1} \cdot \sqrt{8}\):
\[ \sqrt{-8} = i\sqrt{8} \]
2. Now, simplify \(\sqrt{8}\):
\[ \sqrt{8} = \sqrt{4 \cdot 2} = \sqrt{4} \cdot \sqrt{2} = 2\sqrt{2} \]
3. Therefore, we can rewrite \(-3\sqrt{-8}\) as:
\[ -3\sqrt{-8} = -3(i \cdot 2\sqrt{2}) = -6i\sqrt{2} \]

### Step 3: Combine the two results

Now, we combine the results from Step 1 and Step 2:
\[ 2\sqrt{-50} - 3\sqrt{-8} = 10i\sqrt{2} - 6i\sqrt{2} \]
Combine like terms:
\[ = (10i - 6i)\sqrt{2} = 4i\sqrt{2} \]

### Final Answer

Thus, the expression \(2\sqrt{-50} - 3\sqrt{-8}\) in its simplest form is:
\[ \boxed{4i\sqrt{2}} \]