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What is the square root of (x ² y²)?

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Final answer:

The square root of (x²y²) is xy, assuming x and y are non-negative. This simplification occurs because the square root operation cancels out the square (exponent of 2) on both variables.

Step-by-step explanation:

The question asks about the square root of an expression involving variables raised to the power of 2, specifically (x²y²). When you take the square root of a variable raised to the second power, the square root and the square essentially cancel each other out, leaving you with the base variable. Therefore, the square root of (x²y²) simplifies to xy, as long as x and y are non-negative. This is because under the radical sign, the exponents of x and y are both 2, and when you take the square root, you divide the exponents by 2 (the index of the root), which yields x¹y¹ or simply xy.

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