The value of `(root3(8)+root3(27)-root3(343))/((2)^(2)-3)` is

Options

A. 7
B. -2
C. 8
D. -5

Answer

To solve the expression \((\sqrt[3]{8} + \sqrt[3]{27} - \sqrt[3]{343}) / (2^2 - 3)\), we will break it down step by step.

### Step 1: Calculate the cube roots
1. **Calculate \(\sqrt[3]{8}\)**:
\[ \sqrt[3]{8} = \sqrt[3]{2^3} = 2 \]

2. **Calculate \(\sqrt[3]{27}\)**:
\[ \sqrt[3]{27} = \sqrt[3]{3^3} = 3 \]

3. **Calculate \(\sqrt[3]{343}\)**:
\[ \sqrt[3]{343} = \sqrt[3]{7^3} = 7 \]

### Step 2: Substitute the values back into the expression
Now, substitute the calculated values into the expression:
\[ \sqrt[3]{8} + \sqrt[3]{27} - \sqrt[3]{343} = 2 + 3 - 7 \]

### Step 3: Simplify the numerator
Now simplify the numerator:
\[ 2 + 3 - 7 = 5 - 7 = -2 \]

### Step 4: Calculate the denominator
Now calculate the denominator:
\[ 2^2 - 3 = 4 - 3 = 1 \]

### Step 5: Divide the numerator by the denominator
Now divide the simplified numerator by the denominator:
\[ \frac{-2}{1} = -2 \]

### Final Answer
Thus, the value of the expression is:
\[ \boxed{-2} \]