if `x=root3 (13(103)/125)`, then the value of x is

Options

A. `2(1)/5`
B. `2(2)/5`
C. `3(4)/5`
D. `4(1)/5`

Answer

To solve the question \( x = \sqrt[3]{\frac{13 \cdot 103}{125}} \), we will follow these steps:

### Step 1: Calculate the product in the numerator
First, we need to calculate \( 13 \cdot 103 \).

\[ 13 \cdot 103 = 1339 \]

### Step 2: Rewrite the expression
Now we can rewrite \( x \) as follows:

\[ x = \sqrt[3]{\frac{1339}{125}} \]

### Step 3: Simplify the cube root
We know that \( 125 = 5^3 \), so we can rewrite the expression:

\[ x = \sqrt[3]{\frac{1339}{5^3}} = \frac{\sqrt[3]{1339}}{\sqrt[3]{125}} = \frac{\sqrt[3]{1339}}{5} \]

### Step 4: Calculate the cube root of 1339
Since \( 1339 \) is not a perfect cube, we can approximate its cube root. However, for simplicity, we will keep it as \( \sqrt[3]{1339} \).

### Step 5: Final expression for x
Thus, we have:

\[ x = \frac{\sqrt[3]{1339}}{5} \]

### Step 6: Approximate the value of \( \sqrt[3]{1339} \)
To find the approximate value of \( \sqrt[3]{1339} \), we can use a calculator or estimation techniques. The approximate value is around \( 10.9 \).

Now substituting back:

\[ x \approx \frac{10.9}{5} \approx 2.18 \]

### Final Answer
So, the value of \( x \) is approximately \( 2.18 \).

---