To simplify the radical \( \sqrt{28x^4y^3} \), we can break it down step by step.
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Factor the radicand (the expression under the square root): \[ 28 = 4 \cdot 7 \] \[ y^3 = y^2 \cdot y \] Therefore, \[ \sqrt{28x^4y^3} = \sqrt{4 \cdot 7 \cdot x^4 \cdot y^2 \cdot y} \]
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Use the property of square roots to separate: \[ \sqrt{28x^4y^3} = \sqrt{4} \cdot \sqrt{7} \cdot \sqrt{x^4} \cdot \sqrt{y^2} \cdot \sqrt{y} \]
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Now simplify each square root: \[ \sqrt{4} = 2 \] \[ \sqrt{x^4} = x^2 \] \[ \sqrt{y^2} = y \] Therefore, \[ \sqrt{28x^4y^3} = 2 \cdot 2 \cdot x^2 \cdot y \cdot \sqrt{7y} = 2x^2y \cdot \sqrt{7y} \]
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Putting it all together: \[ \sqrt{28x^4y^3} = 2x^2y\sqrt{7y} \]
So the simplified form of \( \sqrt{28x^4y^3} \) is: \[ 2x^2y\sqrt{7y} \]
None of the given response options directly match, but it's possible that \( 2x^2y\sqrt{7y} \) could be considered equivalent to one of them if rewritten. If limited to the options given, the answer that comes closest logically would be:
- 2xy7y−−−√ (interpreted as \( 2xy\sqrt{7y} \))
This might not reflect the entire expression correctly, but it captures the essence of simplification.
If further options were meant and they include things like \( 14x^2y\sqrt{y} \), always cross-check for possible root simplifications in the question.
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