Question

Please help solve this problem

Answer 1

Answer: OPTION C

Step-by-step 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: $\sqrt{x^4}=x^{(\frac{4}{2})}=x^{2}$). Then, you obtain:

$\sqrt{2*3^2*x^4*y*y^2}=3x^2y\sqrt{2y}$

Answer 2

Answer:

C. $3x^2y\sqrt{2y}$.

Step-by-step explanation:

The given radical expression is  $\sqrt{18x^4y^3}$.

We can rewrite this radical expression to obtain;

$\sqrt{2\times9 \times (x^2)^2\times y^2\times y}$.

This will give us;

$\sqrt{2y} \times \sqrt{9(x^2)^2 y^2}$.

$3x^2y\sqrt{2y}$.

The correct choice is C