To simplify \(\sqrt{2x^9}\), we can break it down as follows:
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Separate the square root into components: \[ \sqrt{2x^9} = \sqrt{2} \cdot \sqrt{x^9} \]
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Simplify \(\sqrt{x^9}\): \[ \sqrt{x^9} = \sqrt{x^{8} \cdot x^1} = \sqrt{x^{8}} \cdot \sqrt{x} = x^4 \cdot \sqrt{x} \]
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Rewrite the expression: \[ \sqrt{2x^9} = \sqrt{2} \cdot x^4 \cdot \sqrt{x} = x^4 \sqrt{2x} \]
So, the simplified form of \(\sqrt{2x^9}\) is: \[ x^4 \sqrt{2x} \]
Now let's check the provided multiple choice answers to see which corresponds to our simplification:
- \( x^5 \sqrt{2x} \)
- \( 2x \)
- \( 2x^4 \sqrt{2x} \)
- \( x^4 \sqrt{2x} \)
The correct answer is: \[ x^4 \sqrt{2x} \]