If `x ^(3) = 6 ^(2) - 3 ^(2),` then the value of x is

Options

A. 9
B. 6
C. 3
D. 1

Answer

To solve the equation \( x^3 = 6^2 - 3^2 \), we will follow these steps:

### Step 1: Calculate \( 6^2 \) and \( 3^2 \)
First, we need to find the values of \( 6^2 \) and \( 3^2 \).

\[ 6^2 = 36 \]
\[ 3^2 = 9 \]

### Step 2: Substitute the values into the equation
Now, we substitute these values into the equation:

\[ x^3 = 36 - 9 \]

### Step 3: Perform the subtraction
Next, we perform the subtraction:

\[ x^3 = 27 \]

### Step 4: Find the cube root of both sides
To find the value of \( x \), we take the cube root of both sides:

\[ x = \sqrt[3]{27} \]

### Step 5: Calculate the cube root
The cube root of 27 is:

\[ x = 3 \]

### Final Answer
Thus, the value of \( x \) is \( 3 \).

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