Twice the square of a number is the cube of 18. The number is

Options

A. 54
B. 108
C. 162
D. 324

Answer

To solve the problem, we will follow these steps:

1. **Define the variable**: Let the number be \( x \).

2. **Set up the equation**: According to the problem, "Twice the square of a number is the cube of 18". We can express this mathematically as:
\[ 2x^2 = 18^3 \]

3. **Calculate \( 18^3 \)**: We need to find the value of \( 18^3 \). We can calculate it as:
\[ 18^3 = 18 \times 18 \times 18 \]
First, calculate \( 18 \times 18 = 324 \), then multiply by 18 again:
\[ 324 \times 18 = 5832 \]
So, \( 18^3 = 5832 \).

4. **Substitute back into the equation**: Now we substitute \( 18^3 \) back into our equation:
\[ 2x^2 = 5832 \]

5. **Divide both sides by 2**: To isolate \( x^2 \), we divide both sides of the equation by 2:
\[ x^2 = \frac{5832}{2} = 2916 \]

6. **Take the square root**: Now, we find \( x \) by taking the square root of both sides:
\[ x = \sqrt{2916} \]

7. **Calculate the square root**: We can find \( \sqrt{2916} \). It can be simplified:
\[ 2916 = 54 \times 54 \]
Therefore, \( \sqrt{2916} = 54 \).

8. **Conclusion**: Thus, the number is:
\[ x = 54 \]