How do you simplify #sqrt(27x^2y) - sqrt(45xy^2) +sqrt(108x^2y) - sqrt(125xy^2)#?

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Answer 1 · 2015-05-16T08:53:40

#sqrt(27x^2y)-sqrt(45xy^2)+sqrt(108x^2y)-sqrt(125xy^2)#

#= sqrt(9x^2*3y)-sqrt(9y^2*5x)+sqrt(36x^2*3y)-sqrt(25y^2*5x)#

#= sqrt((3x)^2*3y)-sqrt((3y)^2*5x)+sqrt((6x)^2*3y)-sqrt((5y)^2*5x)#

#= sqrt((3x)^2)sqrt(3y)-sqrt((3y)^2)sqrt(5x)+sqrt((6x)^2)sqrt(3y)-sqrt((5y)^2)sqrt(5x)#

#= 3xsqrt(3y)-3ysqrt(5x)+6xsqrt(3y)-5ysqrt(5x)#

#= (3x+6x)sqrt(3y)-(3y+5y)sqrt(5x)#

#= 9xsqrt(3y)-8xsqrt(5x)#