To simplify the expression \(\sqrt{28x^4y^3}\), let's break it down step by step.
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Factor inside the square root: \[ 28 = 4 \times 7 \] So, we rewrite the expression as: \[ \sqrt{28x^4y^3} = \sqrt{4 \times 7 \times x^4 \times y^3} \]
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Break down the square root: By using the property \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can split the square root: \[ \sqrt{28x^4y^3} = \sqrt{4} \times \sqrt{7} \times \sqrt{x^4} \times \sqrt{y^3} \]
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Calculate the square roots:
- \(\sqrt{4} = 2\)
- \(\sqrt{x^4} = x^2\) (since \(\sqrt{x^m} = x^{m/2}\), and \(4/2 = 2\))
- For \(y^3\), we can express \(\sqrt{y^3} = \sqrt{y^2 \times y} = \sqrt{y^2} \times \sqrt{y} = y \sqrt{y}\)
Putting it all together: \[ \sqrt{28x^4y^3} = 2 \times \sqrt{7} \times x^2 \times y \sqrt{y} \]
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Combine the terms: Now, we can combine all the simplifications together: \[ = 2x^2y \sqrt{7y} \]
So, the simplified form of \(\sqrt{28x^4y^3}\) is: \[ 2x^2y\sqrt{7y} \]
Therefore, the correct response is: \(2x^2y\sqrt{7y}\).
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