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[tex]\sqrt{576 x^4 y^6}\\\\\\=\left(24^2 x^4 y^6\right)^{\tfrac 12}~~~~~~; \left[\sqrt a = a^{\tfrac 12} \right]\\\\\\=(24^2)^{\tfrac 12} \times (x^4)^{\tfrac 12} \times (y^6)^{\tfrac 12}\\\\\\=24^{\tfrac 22} \cdot x^{\tfrac 42} \cdot y^{\tfrac 62}\\\\=24 x^2 y^3[/tex]

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