Question

Which expression is equivalent to 50x5y2−−−−−−√50x5y2 ?(1 point) Responses 10x3y10x3y10 x cubed y 5x2y2x−−√5x2y2x5 x squared y square root of 2 x 5xy2x−−√5xy2x5 x y square root of 2 x 25x2yx−−√

Answer 1

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

1. **Factor the constant and variables**:
\[
\sqrt{50x^5y^2} = \sqrt{(25 \cdot 2) \cdot x^5 \cdot y^2}
\]

2. **Simplify each part**:
- The square root of 25 is 5.
- For \( x^5 \), we take half of the exponent (which gives us \( x^2 \)) and keep one \( x \) inside the square root, so \( \sqrt{x^5} = x^2\sqrt{x} \).
- For \( y^2 \), the square root is simply \( y \).

Putting these pieces together gives:
\[
\sqrt{50x^5y^2} = \sqrt{25} \cdot \sqrt{2} \cdot \sqrt{x^5} \cdot \sqrt{y^2} = 5 \cdot \sqrt{2} \cdot x^2 \cdot y
\]
So, we have:
\[
\sqrt{50x^5y^2} = 5x^2y\sqrt{2}
\]

The expression \( 5x^2y\sqrt{2} \) is equivalent to the option:
\[
5 x^2 y \sqrt{2}
\]

Thus, the answer is \( 5 x^2 y \sqrt{2} \).