Q. Simplify. Remove all perfect squares from inside the square roots. Assume x and y are positive.8x3y2=
Break down prime factors: Break down the square root into prime factors and separate the variables. 8x3y2=23×x3×y2
Separate into individual roots: Separate the square root into individual square roots for each factor.8x3y2=23⋅x3⋅y2
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.23=2×2 because 22 is a perfect square and we are left with one 2 inside the square root.x3=x×x because x2 is a perfect square and we are left with one x inside the square root.y2=y because y2 is a perfect square and there is no remainder inside the square root.
Combine simplified roots: Combine the simplified square roots. 8x3y2=2×2×x×x×y
Combine roots and terms: Combine the square roots and the terms outside the square roots separately. 8x3y2=2xy×2x
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