To simplify \( \sqrt{80x^3y^2} \), we can break it down step by step.
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Factor 80: \( 80 = 16 \cdot 5 = 4^2 \cdot 5 \)
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Rewrite the expression under the square root: \[ \sqrt{80x^3y^2} = \sqrt{16 \cdot 5 \cdot x^3 \cdot y^2} \]
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Now we can simplify each part: \[ \sqrt{16} = 4 \] For \( x^3 \), we can break it down as \( x^2 \cdot x \): \[ \sqrt{x^3} = \sqrt{x^2 \cdot x} = \sqrt{x^2} \cdot \sqrt{x} = x \sqrt{x} \] For \( y^2 \): \[ \sqrt{y^2} = y \]
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Combine all the parts together: \[ \sqrt{80x^3y^2} = 4 \cdot x \cdot y \cdot \sqrt{5x} \] Thus, we have: \[ 4xy\sqrt{5x} \]
So, the simplified form of \( \sqrt{80x^3y^2} \) is \( 4xy\sqrt{5x} \).
The correct response is: 4xy√5x.