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Assuming x and y are both positive, write the following expression in simplest radical form. sqrt(4x^(3)y^(7)) Answer:

Assuming x x and y y are both positive, write the following expression in simplest radical form.\newline4x3y7 \sqrt{4 x^{3} y^{7}} \newlineAnswer:

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Q. Assuming x x and y y are both positive, write the following expression in simplest radical form.\newline4x3y7 \sqrt{4 x^{3} y^{7}} \newlineAnswer:
  1. Identify Perfect Squares: Identify the perfect squares within the radicand. The radicand is 4x3y74x^3y^7. We can see that 44 is a perfect square, x3x^3 contains a perfect square (x2x^2), and y7y^7 contains a perfect square (y6y^6).
  2. Rewrite Radicand: Rewrite the radicand by separating the perfect squares from the non-perfect squares. 4x3y7=4×x2×x×y6×y\sqrt{4x^3y^7} = \sqrt{4 \times x^2 \times x \times y^6 \times y}
  3. Take Square Roots: Take the square root of the perfect squares and leave the non-perfect squares inside the radical. 4×x2×y6×x×y\sqrt{4} \times \sqrt{x^2} \times \sqrt{y^6} \times \sqrt{x} \times \sqrt{y} = 2×x×y3×x×y2 \times x \times y^3 \times \sqrt{x} \times \sqrt{y}
  4. Combine Square Roots: Combine the square roots of the non-perfect squares. 2×x×y3×xy2 \times x \times y^3 \times \sqrt{xy}
  5. Write Final Expression: Write the final expression in simplest radical form.\newlineThe simplest radical form of the expression is 2xy3xy2xy^3\sqrt{xy}.

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