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Assuming 
x and 
y are both positive, write the following expression in simplest radical form.

8ysqrt(20x^(2)y^(4))
Answer:

Assuming x x and y y are both positive, write the following expression in simplest radical form.\newline8y20x2y4 8 y \sqrt{20 x^{2} y^{4}} \newlineAnswer:

Full solution

Q. Assuming x x and y y are both positive, write the following expression in simplest radical form.\newline8y20x2y4 8 y \sqrt{20 x^{2} y^{4}} \newlineAnswer:
  1. Factor and Separate: We start by factoring the expression inside the square root to separate perfect squares from non-perfect squares. 8y20x2y4=8y45x2y48y\sqrt{20x^{2}y^{4}} = 8y\sqrt{4\cdot 5x^{2}y^{4}}
  2. Take Square Roots: Now we can take the square root of the perfect squares. The square root of 44 is 22, the square root of x2x^2 is xx, and the square root of y4y^4 is y2y^2. 8y45x2y4=8y2xy258y\sqrt{4\cdot 5x^{2}y^{4}} = 8y \cdot 2xy^2 \cdot \sqrt{5}
  3. Multiply Constants and Like Terms: Next, we multiply the constants and the like terms outside the square root. 8y×2xy2=16x×y38y \times 2xy^2 = 16x \times y^3
  4. Combine Terms: Now we combine the constant and variable terms with the remaining square root. 16xy35=16xy3516x \cdot y^3 \cdot \sqrt{5} = 16xy^3\sqrt{5}
  5. Simplify Expression: We have simplified the expression to its simplest radical form.