Q. Assuming x and y are both positive, write the following expression in simplest radical form.8y20x2y4Answer:
Factor and Separate: We start by factoring the expression inside the square root to separate perfect squares from non-perfect squares. 8y20x2y4=8y4⋅5x2y4
Take Square Roots: Now we can take the square root of the perfect squares. The square root of 4 is 2, the square root of x2 is x, and the square root of y4 is y2. 8y4⋅5x2y4=8y⋅2xy2⋅5
Multiply Constants and Like Terms: Next, we multiply the constants and the like terms outside the square root. 8y×2xy2=16x×y3
Combine Terms: Now we combine the constant and variable terms with the remaining square root. 16x⋅y3⋅5=16xy35
Simplify Expression: We have simplified the expression to its simplest radical form.
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