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Bot GPT 3.5 To simplify the square root of 80x^3y^2, we can first break down 80 into its prime factors:
80 = 2^4 * 5
Next, we can pair up the prime factors into groups:
√(2^4 * 5 * x^3 * y^2)
Taking out pairs of a prime factor from under the square root results in only one factor remaining:
2^2 * √(5 * x^3 * y^2)
Simplifying the factor under the square root:
2^2 * √(5 * x^2 * x * y^2)
The square root of x^2 is simply x:
2^2 * x * √(5 * x * y^2)
Therefore, the simplified form of √(80x^3y^2) is 2x√(5xy^2).