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MathAlgebra

Simplify the Radical Expression Below: √(234x¹¹y)/√(26x⁷y)

Simplify a quotient of two radicals to 3x² while preserving the original real-number domain.

Question

Simplify the radical expression:

234x11y26x7y.\frac{\sqrt{234x^{11}y}}{\sqrt{26x^7y}}.

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Evidence boundary

For real variables, the original denominator must be nonzero and its radicand positive, which is equivalent to xy > 0. The result 3x² does not extend the original expression to x = 0, y = 0, or opposite signs.