Assuming xx and yy are both positive, write the following expression in simplest radical form.4, x, y, squared, square root of, 25, x, to the power 4 , y, cubed, end square root4xy 2 25x 4 y 3
Question
Assuming xx and yy are both positive, write the following expression in simplest radical form.4, x, y, squared, square root of, 25, x, to the power 4 , y, cubed, end square root4xy 2 25x 4 y 3
Solution
The given expression is:
√(4x^2y^2 * 25x^4y^3)
Step 1: Simplify inside the square root first. Multiply the numbers and then apply the product rule of exponents (a^m * a^n = a^(m+n)) to the variables.
= √(100x^6y^5)
Step 2: Break down the expression inside the square root into its prime factors.
= √(2^2 * 5^2 * x^6 * y^5)
Step 3: Apply the rule √(a^2) = a to simplify the square root.
= 10x^3y^2 * √(y)
So, the expression in simplest radical form is 10x^3y^2√y.
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