If ` a^(1/3) = 11` , then the value of `a^2 - 331 a ` is

Options

A. 1331331
B. 1331000
C. 1334331
D. 1330030

Answer

To solve the problem step by step, we start with the given equation:

1. **Given Equation**:
\[ a^{1/3} = 11 \]

2. **Finding the Value of \( a \)**:
To find \( a \), we can cube both sides of the equation:
\[ a = (11)^3 \]
Now calculate \( 11^3 \):
\[ 11^3 = 11 \times 11 \times 11 = 121 \times 11 = 1331 \]
So, we have:
\[ a = 1331 \]

3. **Substituting \( a \) into the Expression**:
We need to find the value of \( a^2 - 331a \). First, calculate \( a^2 \):
\[ a^2 = (1331)^2 \]
To calculate \( 1331^2 \):
\[ 1331^2 = 1771561 \]
Now calculate \( 331a \):
\[ 331a = 331 \times 1331 \]
To calculate \( 331 \times 1331 \):
\[ 331 \times 1331 = 440561 \]

4. **Final Calculation**:
Now substitute back into the expression:
\[ a^2 - 331a = 1771561 - 440561 \]
Now perform the subtraction:
\[ 1771561 - 440561 = 1331000 \]

Thus, the final answer is:
\[ \boxed{1331000} \]