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Simplify.
Remove all perfect squares from inside the square roots. Assume 
x and 
y are positive.

sqrt(8x^(3)y^(2))=

Simplify. Remove all perfect squares from inside the square roots. Assume xx and yy are positive.\newline8x3y2\sqrt{8x^{3}y^{2}}=

Full solution

Q. Simplify. Remove all perfect squares from inside the square roots. Assume xx and yy are positive.\newline8x3y2\sqrt{8x^{3}y^{2}}=
  1. Break down prime factors: Break down the square root into prime factors and separate the variables. 8x3y2=23×x3×y2\sqrt{8x^{3}y^{2}} = \sqrt{2^{3} \times x^{3} \times y^{2}}
  2. Separate into individual roots: Separate the square root into individual square roots for each factor.8x3y2=23x3y2\sqrt{8x^{3}y^{2}} = \sqrt{2^{3}} \cdot \sqrt{x^{3}} \cdot \sqrt{y^{2}}
  3. Simplify perfect squares: Simplify the square roots of the perfect squares and take one factor out of the square root for the non-perfect squares.\newline23=2×2\sqrt{2^3} = 2 \times \sqrt{2} because 222^2 is a perfect square and we are left with one 22 inside the square root.\newlinex3=x×x\sqrt{x^3} = x \times \sqrt{x} because x2x^2 is a perfect square and we are left with one xx inside the square root.\newliney2=y\sqrt{y^2} = y because y2y^2 is a perfect square and there is no remainder inside the square root.
  4. Combine simplified roots: Combine the simplified square roots. 8x3y2=2×2×x×x×y\sqrt{8x^{3}y^{2}} = 2 \times \sqrt{2} \times x \times \sqrt{x} \times y
  5. Combine roots and terms: Combine the square roots and the terms outside the square roots separately. 8x3y2=2xy×2x\sqrt{8x^{3}y^{2}} = 2xy \times \sqrt{2x}

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