Question

Question
Which expression is equivalent to √50x^5y^2
?(1 point)
Responses

5x^2y√2x
5 x squared y square root of 2 x
5xy√2x
5 x y square root of 2 x
10^x3y
10 x cubed y
25x^2y√x

Answer 1

To simplify the expression \( \sqrt{50x^5y^2} \), we can break it down as follows:

1. **Factor the radicand**:
\[
50 = 25 \cdot 2
\]
\[
x^5 = x^4 \cdot x = (x^2)^2 \cdot x
\]
\[
y^2 = (y)^2
\]
Therefore,
\[
\sqrt{50x^5y^2} = \sqrt{25 \cdot 2 \cdot x^4 \cdot x \cdot y^2}
\]

2. **Apply the property of square roots**:
\[
\sqrt{a \cdot b} = \sqrt{a} \cdot \sqrt{b}
\]
Thus,
\[
\sqrt{50x^5y^2} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{x^4} \cdot \sqrt{x} \cdot \sqrt{y^2}
\]

3. **Evaluate the square roots**:
\[
\sqrt{25} = 5
\]
\[
\sqrt{x^4} = x^2
\]
\[
\sqrt{y^2} = y
\]
So now we have:
\[
\sqrt{50x^5y^2} = 5 \cdot \sqrt{2} \cdot x^2 \cdot y \cdot \sqrt{x}
\]

4. **Combine**:
We can write this as:
\[
5x^2y \cdot \sqrt{2x}
\]

This means that the expression \( \sqrt{50x^5y^2} \) simplifies to \( 5x^2y\sqrt{2x} \).

Thus, the correct response is:
**5x²y√2x**