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Assuming x and y are both positive, write the following expression in simplest radical form. x^(2)sqrt(75x^(3)y^(6)) Answer:

Assuming x x and y y are both positive, write the following expression in simplest radical form.\newlinex275x3y6 x^{2} \sqrt{75 x^{3} y^{6}} \newlineAnswer:

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Q. Assuming x x and y y are both positive, write the following expression in simplest radical form.\newlinex275x3y6 x^{2} \sqrt{75 x^{3} y^{6}} \newlineAnswer:
  1. Factor and Simplify: First, we will factor the number 7575 inside the square root to prime factors to see if any can be taken out of the square root.75=3×25=3×5275 = 3 \times 25 = 3 \times 5^2
  2. Rewrite and Simplify Square Roots: Next, we will rewrite the square root of the product as the product of square roots, and then simplify the square roots of the perfect squares.\newline75x3y6=3×52×x2×x×y6\sqrt{75x^{3}y^{6}} = \sqrt{3 \times 5^2 \times x^2 \times x \times y^6}\newline=3×52×x2×x×y6= \sqrt{3} \times \sqrt{5^2} \times \sqrt{x^2} \times \sqrt{x} \times \sqrt{y^6}\newline=5×x×y3×3×x= 5 \times x \times y^3 \times \sqrt{3} \times \sqrt{x}
  3. Multiply by x2x^2: Now, we will multiply the simplified square root by x2x^2.x2×(5×x×y3×3×x)=5×x3×y3×3×xx^2 \times (5 \times x \times y^3 \times \sqrt{3} \times \sqrt{x}) = 5 \times x^3 \times y^3 \times \sqrt{3} \times \sqrt{x}
  4. Combine and Simplify: Finally, we will combine the square roots and write the expression in its simplest radical form. 5×x3×y3×3x5 \times x^3 \times y^3 \times \sqrt{3x}

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