Question

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

Answer 1

`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`