How do you simplify $\sqrt{27 x^{2} y} - \sqrt{45 x y^{2}} + \sqrt{108 x^{2} y} - \sqrt{125 x y^{2}}$ $sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)$ ?

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How do you simplify $\sqrt{27 x^{2} y} - \sqrt{45 x y^{2}} + \sqrt{108 x^{2} y} - \sqrt{125 x y^{2}}$ $sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)$ ?

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Answer 1 · 2015-05-16T08:53:40

$\sqrt{27 x^{2} y} - \sqrt{45 x y^{2}} + \sqrt{108 x^{2} y} - \sqrt{125 x y^{2}}$ $sqrt(27x^2y)-sqrt(45xy^2)+sqrt(108x^2y)-sqrt(125xy^2)$

$= \sqrt{9 x^{2} \cdot 3 y} - \sqrt{9 y^{2} \cdot 5 x} + \sqrt{36 x^{2} \cdot 3 y} - \sqrt{25 y^{2} \cdot 5 x}$ $= sqrt(9x^2*3y)-sqrt(9y^2*5x)+sqrt(36x^2*3y)-sqrt(25y^2*5x)$

$= \sqrt{{(3 x)}^{2} \cdot 3 y} - \sqrt{{(3 y)}^{2} \cdot 5 x} + \sqrt{{(6 x)}^{2} \cdot 3 y} - \sqrt{{(5 y)}^{2} \cdot 5 x}$ $= sqrt((3x)^2*3y)-sqrt((3y)^2*5x)+sqrt((6x)^2*3y)-sqrt((5y)^2*5x)$

$= \sqrt{{(3 x)}^{2}} \sqrt{3 y} - \sqrt{{(3 y)}^{2}} \sqrt{5 x} + \sqrt{{(6 x)}^{2}} \sqrt{3 y} - \sqrt{{(5 y)}^{2}} \sqrt{5 x}$ $= sqrt((3x)^2)sqrt(3y)-sqrt((3y)^2)sqrt(5x)+sqrt((6x)^2)sqrt(3y)-sqrt((5y)^2)sqrt(5x)$

$= 3 x \sqrt{3 y} - 3 y \sqrt{5 x} + 6 x \sqrt{3 y} - 5 y \sqrt{5 x}$ $= 3xsqrt(3y)-3ysqrt(5x)+6xsqrt(3y)-5ysqrt(5x)$

$= (3 x + 6 x) \sqrt{3 y} - (3 y + 5 y) \sqrt{5 x}$ $= (3x+6x)sqrt(3y)-(3y+5y)sqrt(5x)$

$= 9 x \sqrt{3 y} - 8 x \sqrt{5 x}$ $= 9xsqrt(3y)-8xsqrt(5x)$

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How do you simplify $\sqrt{27 x^{2} y} - \sqrt{45 x y^{2}} + \sqrt{108 x^{2} y} - \sqrt{125 x y^{2}}$ $sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)$ ?

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How do you simplify sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)√27x2y−√45xy2+√108x2y−√125xy2sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)?

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How do you simplify $\sqrt{27 x^{2} y} - \sqrt{45 x y^{2}} + \sqrt{108 x^{2} y} - \sqrt{125 x y^{2}}$ $sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)$ ?