Simplify 80x3y2−−−−−−√

Question

(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.