To determine which of the given radical expressions simplifies to \( 2x , 15y \), we can simplify each expression one by one.
-
Expression: \( 5\sqrt{6xy^2} \)
\[ 5\sqrt{6xy^2} = 5\sqrt{6} \cdot \sqrt{x} \cdot \sqrt{y^2} = 5\sqrt{6} \cdot \sqrt{x} \cdot y \]
This does not simplify directly to \( 2x , 15y \).
-
Expression: \( 3\sqrt{50x^2y} \)
\[ \sqrt{50} = \sqrt{25 \cdot 2} = 5\sqrt{2} \ 3\sqrt{50x^2y} = 3 \cdot 5\sqrt{2} \cdot \sqrt{x^2} \cdot \sqrt{y} = 15\sqrt{2} \cdot x \cdot \sqrt{y} \]
This does not simplify directly to \( 2x , 15y \).
-
Expression: \( 60x^2y \)
This expression is already simplified and is not in a radical form. However, when compared, it does not resemble \( 2x , 15y \) (which is \( 30xy \) when simplified).
-
Expression: \( \sqrt{30x^2y} \)
\[ \sqrt{30x^2y} = \sqrt{30} \cdot \sqrt{x^2} \cdot \sqrt{y} = \sqrt{30} \cdot x \cdot \sqrt{y} \]
Clearly, this does not simplify to \( 2x , 15y \).
Looking at the expression \( 2x , 15y \) itself gives us \( 30xy \) since \( 2 \times 15 = 30 \).
None of the provided expressions directly simplify to \( 30xy \). Thus, there isn't an option listed that simplifies to match \( 2x , 15y \).
In summary, none of the given options are valid expressions that simplify to \( 2x , 15y \). Please check the expressions or the required answer once again.