Simplify the radical.

Question

28x4y3
(1 point)
○ 14x²y√√y
2xy√7xy
4x²y√7y
2x²y√ √7y

Answer 1

To simplify the expression \(\sqrt{28x^4y^3}\), we can break it down step by step.

1. Factor the radicand: \[ 28 = 4 \times 7 \] \[ x^4 = (x^2)^2 \] \[ y^3 = y^2 \cdot y \]

   So: \[ \sqrt{28x^4y^3} = \sqrt{4 \cdot 7 \cdot (x^2)^2 \cdot y^2 \cdot y} \]

2. Use properties of square roots: \[ = \sqrt{4} \cdot \sqrt{(x^2)^2} \cdot \sqrt{y^2} \cdot \sqrt{7y} \] \[ = 2 \cdot x^2 \cdot y \cdot \sqrt{7y} \]

3. Combine the terms: \[ = 2x^2y\sqrt{7y} \]

Thus, the simplified form is: \[ 2x^2y\sqrt{7y} \]

So your answer is 2x²y√7y.