It seems like you've provided an expression to simplify, but the expression isn't clearly formatted, and it appears that the options (A, B, C, D) are not listed. Let’s simplify the expression you've provided, \( 2\sqrt[3]{54} - \sqrt{18} \), and then if you provide the options, I can help you determine which is equivalent.
First, let's simplify \( 2\sqrt[3]{54} \):
- Factor \( 54 \) as \( 54 = 2 \times 3^3 \).
- Therefore, \( \sqrt[3]{54} = \sqrt[3]{2 \times 3^3} = \sqrt[3]{2} \cdot 3 \).
- Thus, \( 2\sqrt[3]{54} = 2 \cdot 3\sqrt[3]{2} = 6\sqrt[3]{2} \).
Now, let's simplify \( \sqrt{18} \):
- Factor \( 18 \) as \( 18 = 9 \times 2 \).
- Therefore, \( \sqrt{18} = \sqrt{9 \times 2} = \sqrt{9} \cdot \sqrt{2} = 3\sqrt{2} \).
Now put it all together:
\[ 2\sqrt[3]{54} - \sqrt{18} = 6\sqrt[3]{2} - 3\sqrt{2} \]
This gives us a simplified expression of \( 6\sqrt[3]{2} - 3\sqrt{2} \).
If you provide the options (A, B, C, D), I can help you find out which one is equivalent to this expression!
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