`2root(3)(32)-3root(3)(4)+root(3)(500)` is equal to :

Options

A. `4root(3)(6)`
B. `3sqrt(24)`
C. `6root(3)(4)`
D. `916`

Answer

To solve the expression \( 2\sqrt[3]{32} - 3\sqrt[3]{4} + \sqrt[3]{500} \), we will simplify each term step by step.

### Step 1: Simplify \( 2\sqrt[3]{32} \)

We can express \( 32 \) as \( 8 \times 4 \), where \( 8 \) is a perfect cube.
\[ \sqrt[3]{32} = \sqrt[3]{8 \times 4} = \sqrt[3]{8} \times \sqrt[3]{4} = 2\sqrt[3]{4} \]
Now, substituting this back into the expression:
\[ 2\sqrt[3]{32} = 2 \times 2\sqrt[3]{4} = 4\sqrt[3]{4} \]

### Step 2: Simplify \( 3\sqrt[3]{4} \)

This term is already in its simplest form:
\[ 3\sqrt[3]{4} \]

### Step 3: Simplify \( \sqrt[3]{500} \)

We can express \( 500 \) as \( 125 \times 4 \), where \( 125 \) is also a perfect cube.
\[ \sqrt[3]{500} = \sqrt[3]{125 \times 4} = \sqrt[3]{125} \times \sqrt[3]{4} = 5\sqrt[3]{4} \]

### Step 4: Combine all the terms

Now we can combine all the simplified terms:
\[ 4\sqrt[3]{4} - 3\sqrt[3]{4} + 5\sqrt[3]{4} \]
Combining these gives:
\[ (4 - 3 + 5)\sqrt[3]{4} = 6\sqrt[3]{4} \]

### Final Answer

Thus, the expression \( 2\sqrt[3]{32} - 3\sqrt[3]{4} + \sqrt[3]{500} \) simplifies to:
\[ \boxed{6\sqrt[3]{4}} \]