Question

Please help solve this problem

Answer 1

C.
`3x^2y√(2y)`.

Explanation:

The given radical expression is
`√(18x^4y^3)`.

We can rewrite this radical expression to obtain;

`√(2*9 * (x^2)^2* y^2* y)`.

This will give us;

`√(2y) * √(9(x^2)^2 y^2)`.

`3x^2y√(2y)`.

The correct choice is C

Answer 2

Answer: OPTION C

Explanation:

By definition you know that:

`\sqrt[n]{a^n}=a`

and by the exponents properties you also know that:

`a^n*a^m=a^((n+m))`

Now, descompose 18 into its prime factors:

18=2*3*3=2*3²

Rewrite the expression and simplify (Keep on mind that:
`√(x^4)=x^{((4)/(2))}=x^(2)`). Then, you obtain:

`√(2*3^2*x^4*y*y^2)=3x^2y√(2y)`