Question

Match each question with one of the responses

Answer 1

`√(2) \,√(3) \,√(3) =3\,√(2)`

`√(2) \,√(3) \,√(-3) =3\,i\,√(2)`

`√(-2) \,√(-3) \,√(-3) =-3\,i\,√(2)`

4)
`√(2) \,√(-3) \,√(-3) =-3\,√(2)`

Explanation:

Let's work on each expression at a time, recalling the definition of the imaginary unit
`√(-1) =i`, and the properties of radical multiplication:
`√(a) \,\,√(b) =√(a\,b)`

1)
`√(2) \,√(3) \,√(3) =√(2) \,√(3\,*\,3)=√(2) \,√(3^2)=√(2) \,*\,3=3\,√(2)`

2)
`√(2) \,√(3) \,√(-3) =√(2) \,√(3)\,\,√(3) \,\,√(-1) =√(2) \,√(3^2)\,\,i=3\,i\,√(2)`

3)
`√(-2) \,√(-3) \,√(-3) =√(-1) \,\,√(2)\,\, √(-1) \,\,√(3)\,\,√(-1) \,\,√(3)=i^3\,√(2) \,\,√(3^2) =(-1)\,i\,√(2)\,\,3=-3\,i\,√(2)`

4)
`√(2) \,√(-3) \,√(-3) =√(2) \,\,√(-1) \,\,√(3) \,\,√(-1) \,\,√(3) \,=√(2) \,\,i^2 \,\,√(3)  \,\,√(3) \,\,=(-1)\,√(2) \,\,√(3^2) =-3\,√(2)`