if `root3(x-12)=19` ,then the value of x is

Options

A. 6871
B. 6072
C. 6889
D. 5080

Answer

To solve the equation \( \sqrt[3]{x - 12} = 19 \), we will follow these steps:

### Step 1: Remove the cube root
To eliminate the cube root, we will cube both sides of the equation.

\[ (\sqrt[3]{x - 12})^3 = 19^3 \]

### Step 2: Simplify the left side
Using the property of exponents, we simplify the left side:

\[ x - 12 = 19^3 \]

### Step 3: Calculate \( 19^3 \)
Now, we will calculate \( 19^3 \):

\[ 19^3 = 19 \times 19 \times 19 \]

Calculating step by step:

1. \( 19 \times 19 = 361 \)
2. \( 361 \times 19 = 6859 \)

So,

\[ x - 12 = 6859 \]

### Step 4: Solve for \( x \)
Now, we will add 12 to both sides to find \( x \):

\[ x = 6859 + 12 \]

Calculating this gives:

\[ x = 6871 \]

### Final Answer
Thus, the value of \( x \) is \( 6871 \).

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