To simplify the expression \( 3027\sqrt{-63\sqrt{} }\), we first need to address the term under the square root.
Given that \( -63 \) is under the square root, it can be expressed as:
\[ \sqrt{-63} = \sqrt{63} \cdot \sqrt{-1} = \sqrt{63} i \]
Next, \( \sqrt{63} \) can be simplified further:
\[ \sqrt{63} = \sqrt{9 \cdot 7} = \sqrt{9} \cdot \sqrt{7} = 3\sqrt{7} \]
Now, substituting this back into our expression, we have:
\[ \sqrt{-63} = 3\sqrt{7} i \]
Thus, the expression simplifies to:
\[ 3027 \cdot 3\sqrt{7} i = 9081\sqrt{7} i \]
Since this expression is a complex number, it's not one of the regular responses (−3, −15, 15, 3). If you're looking for a numerical answer involving only real numbers, we could say that the expression contains an imaginary component and cannot be simplified into just real numbers.
Please let me know if you were looking for something different!
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