Question

Which of the following radical expressions simplifies to the answer below?

expression: 2x√15y

3√50x^2y
√60x^2y
5√6xy^2
√30x^2y

what is 100% the correct option?

Answer 1

To determine which radical expression simplifies to \( 2x\sqrt{15y} \), we will simplify each of the given options one by one.

1. **Option: \(3\sqrt{50x^2y}\)**

First, simplify \( \sqrt{50x^2y} \):
\[
\sqrt{50x^2y} = \sqrt{25 \cdot 2 \cdot x^2 \cdot y} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{x^2} \cdot \sqrt{y} = 5 \cdot \sqrt{2} \cdot x \cdot \sqrt{y} = 5x\sqrt{2y}
\]
Now multiply by 3:
\[
3\sqrt{50x^2y} = 3 \cdot 5x\sqrt{2y} = 15x\sqrt{2y}
\]

2. **Option: \(\sqrt{60x^2y}\)**

Simplifying \( \sqrt{60x^2y} \):
\[
\sqrt{60x^2y} = \sqrt{4 \cdot 15 \cdot x^2 \cdot y} = \sqrt{4} \cdot \sqrt{15} \cdot \sqrt{x^2} \cdot \sqrt{y} = 2 \cdot \sqrt{15} \cdot x \cdot \sqrt{y} = 2x\sqrt{15y}
\]

This simplifies directly to \(2x\sqrt{15y}\).

3. **Option: \(5\sqrt{6xy^2}\)**

Simplifying \( \sqrt{6xy^2} \):
\[
\sqrt{6xy^2} = \sqrt{6} \cdot \sqrt{x} \cdot \sqrt{y^2} = \sqrt{6} \cdot \sqrt{x} \cdot y
\]
Now multiply by 5:
\[
5\sqrt{6xy^2} = 5y\sqrt{6x}
\]

4. **Option: \(\sqrt{30x^2y}\)**

Simplifying \( \sqrt{30x^2y} \):
\[
\sqrt{30x^2y} = \sqrt{30} \cdot \sqrt{x^2} \cdot \sqrt{y} = \sqrt{30} \cdot x \cdot \sqrt{y}
\]

Now comparing all the simplified forms:

- \( 15x\sqrt{2y} \) from option 1,
- \( 2x\sqrt{15y} \) from option 2,
- \( 5y\sqrt{6x} \) from option 3,
- \( \sqrt{30}x\sqrt{y} \) from option 4.

Only option **2: \( \sqrt{60x^2y} \)** simplifies to \( 2x\sqrt{15y} \).

Thus, **the correct option is**: \(\sqrt{60x^2y}\).