if `root3((156+x))=12`,them the value of x is

Options

A. 1570
B. 1572
C. 1560
D. 1512

Answer

To solve the equation \( \sqrt[3]{156 + x} = 12 \), we will follow these steps:

### Step 1: Cube both sides of the equation
To eliminate the cube root, we will cube both sides of the equation:
\[ (\sqrt[3]{156 + x})^3 = 12^3 \]

### Step 2: Simplify the left side and calculate the right side
Cubing the left side gives us:
\[ 156 + x = 12^3 \]
Now, calculate \( 12^3 \):
\[ 12^3 = 12 \times 12 \times 12 = 144 \times 12 = 1728 \]
So we have:
\[ 156 + x = 1728 \]

### Step 3: Isolate \( x \)
Now, we will isolate \( x \) by subtracting 156 from both sides:
\[ x = 1728 - 156 \]

### Step 4: Perform the subtraction
Now, calculate \( 1728 - 156 \):
\[ 1728 - 156 = 1572 \]

### Conclusion
Thus, the value of \( x \) is:
\[ \boxed{1572} \]

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