Question
Which of the following radical expressions simplifies to the
answer below?
2x 15y
(1 point)
○ 5√6xy2
3√50x2y
60x2y
√√30x²y
answer below?
2x 15y
(1 point)
○ 5√6xy2
3√50x2y
60x2y
√√30x²y
Answers
GPT-4o mini
To determine which of the given radical expressions simplifies to \( 2x \, 15y \), we can simplify each expression one by one.
1. **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 \( 2x \, 15y \).
2. **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 \( 2x \, 15y \).
3. **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).
4. **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.
1. **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 \( 2x \, 15y \).
2. **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 \( 2x \, 15y \).
3. **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).
4. **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.