Assuming x and y are both positive, write the following expression in simplest radical form. 2sqrt(27x^(3)y^(4)) Answer:

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Assuming  x and  y are both positive, write the following expression in simplest radical form.  2sqrt(27x^(3)y^(4)) Answer:

Bytelearn · Accepted Answer

Break down radicand: Break down the radicand into prime factors and perfect squares. We have the expression 2sqrt(27x^(3)y^(4)). Let's first focus on the radicand (the number inside the square root), which is 27x^(3)y^(4). We can break down 27 into its prime factors and express x^(3) and y^(4) in a way that will help us simplify the square root. 27 = 3^3 x^(3) can be written as x^(2) * x, where x^(2) is a perfect square. y^(4) is already a perfect square since (y^2)^2 = y^(4).Simplify using perfect squares: Simplify the square root using the perfect squares. Now we can rewrite the radicand using the perfect squares we identified: sqrt(27x^(3)y^(4)) = sqrt((3^3)(x^(2) * x)(y^(4))) Since we know that sqrt(a^2) = a, we can take out the perfect squares from under the square root: sqrt(27x^(3)y^(4)) = sqrt((3^2 * 3)(x^(2))(y^(2)^2)) = sqrt(9 * 3 * x^(2) * y^(4)) = sqrt(9) * sqrt(3) * sqrt(x^(2)) * sqrt(y^(4)) = 3 * sqrt(3) * x * y^(2)Multiply by coefficient: Multiply the simplified square root by the coefficient outside the square root. We now have the simplified square root, which we need to multiply by the coefficient 2 that is outside the square root in the original expression: 2 * (3 * sqrt(3) * x * y^(2)) = 6 * sqrt(3) * x * y^(2)

Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $2 \sqrt{27 x^{3} y^{4}}$ $\newline$ Answer:

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Assuming $x$ and $y$ are both positive, write the following expression in simplest radical form. $\newline$ $2 \sqrt{27 x^{3} y^{4}}$ $\newline$ Answer: