Simplify √(49x^2 y^2-64x^2 y^2 )+∛(27x^3 y^3 )

asked by guest
on Nov 17, 2024 at 2:37 am



You asked:

Simplify the expression: 49x2y2−64x2y2+27x3y33\sqrt{49 {x}^{2} {y}^{2} - 64 {x}^{2} {y}^{2}} + \sqrt[3]{27 {x}^{3} {y}^{3}}

MathBot Answer:

Simplified:

49x2y2−64x2y2+27x3y33=3x3y33+15−x2y2 \sqrt{49 {x}^{2} {y}^{2} - 64 {x}^{2} {y}^{2}} + \sqrt[3]{27 {x}^{3} {y}^{3}} = 3 \sqrt[3]{x^{3} y^{3}} + \sqrt{15} \sqrt{- x^{2} y^{2}}

27x3y33+49x2y2−64x2y2=3x3y33+49x2y2−64x2y2=3x3y33+−15x2y2=3x3y33+15−x2y2\begin{aligned}\sqrt[3]{27 x^{3} y^{3}} + \sqrt{49 x^{2} y^{2} - 64 x^{2} y^{2}}&=3 \sqrt[3]{x^{3} y^{3}} + \sqrt{49 x^{2} y^{2} - 64 x^{2} y^{2}}\\&=3 \sqrt[3]{x^{3} y^{3}} + \sqrt{- 15 x^{2} y^{2}}\\&=3 \sqrt[3]{x^{3} y^{3}} + \sqrt{15} \sqrt{- x^{2} y^{2}}\end{aligned}

Expanded:

49x2y2−64x2y2+27x3y33=3x3y33+15−x2y2 \sqrt{49 {x}^{2} {y}^{2} - 64 {x}^{2} {y}^{2}} + \sqrt[3]{27 {x}^{3} {y}^{3}} = 3 \sqrt[3]{x^{3} y^{3}} + \sqrt{15} \sqrt{- x^{2} y^{2}}


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