How do you simplify sqrt ((75xy^7)/(12xy))?

1 Answer
Abhinav T.
Jul 23, 2016

5/2 y^3

Explanation:

sqrt((75xy^7)/(12xy))
=sqrt((cancel(3)*25*cancel(x)*cancel(y)*y^6)/(cancel(3)*4*cancel(x)*cancel(y)) {cancelling out common terms in numerator and denominator, and using law of indices x^a*x^b = x^(a+b)}
=sqrt((5y^3)^2/2^2)
=(5/2 y^3)^(2*1/2){using the fact that square roots are same as power 1/2, cube roots as power 1/3 and nth roots are same as power 1/n}
=5/2 y^3

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