Question

Simplify 80x3y2−−−−−−√
(1 point)
Responses

5xy4x−−√
5 x y square root of 4 x

5x2y24x−−√
5 x squared y squared square root of 4 x

4xy5x−−√
4 x y square root of 5 x

4x2y25x−−√
4 x squared y squared square root of 5 x

Answer 1

To simplify the expression \( \sqrt{80x^3y^2} \), we can break it down step by step.

1. **Factor 80**:
\( 80 = 16 \times 5 = 4^2 \times 5 \)

2. **Rewrite the expression**:
\[
\sqrt{80x^3y^2} = \sqrt{16 \cdot 5 \cdot x^3 \cdot y^2}
\]

3. **Apply the square root to each factor**:
\[
\sqrt{16} \cdot \sqrt{5} \cdot \sqrt{x^3} \cdot \sqrt{y^2}
\]

4. **Calculate the square roots**:
- \( \sqrt{16} = 4 \)
- \( \sqrt{x^3} = \sqrt{x^2 \cdot x} = x \sqrt{x} \)
- \( \sqrt{y^2} = y \)

5. **Combine the results**:
\[
4 \cdot y \cdot x \sqrt{x} \cdot \sqrt{5} = 4xy \sqrt{5x}
\]

Thus, the simplified form of \( \sqrt{80x^3y^2} \) is:
\[
4xy\sqrt{5x}
\]

So, the correct option is:
**4x²y²√5x**.