Simplify: The sqrt of 21x^2y/75xy^5

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tiburtius eNotes educator| Certified Educator

`sqrt((21x^2y)/(75xy^5))=sqrt((7x)/(25y^4))=(sqrt(7x))/(sqrt(25y^4))=(sqrt(7x))/(5y^2)`` `` `

oldnick | Student

`sqrt((21x^2y)/(75xy^5))=` `((21/75)(x^2/x)(y/y^5))^(1/2)=` `(7/25)xy^(-4))^(1/2)=`

`=((7x)/25y^4)^(1/2)=((7x)^(1/2))/(25y^4)^(1/2)=`

`((7)^(1/2)x^(1/2))/((5^2)^(1/2)(y^4)^(1/2))=`

`=((7)^(1/2)x^(1/2))/((5)^((2)(1/2))(y)^((4)(1/2)))=`

`=(7^(1/2)x(1/2))/(5y^2)=`

`=sqrt(7x)/(5y^2)`

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