Question

Simplify the radical. 28x4y3−−−−−−√28x4y3 (1 point) Responses 14x2yy√14x2yy14 x squared y square root of y 4x2y7y−−√4x2y7y4 x squared y square root of 7 y 2xy7xy−−−√2xy7xy2 x y square root of 7 x y end root 2x2y7y−−√

Answer 1

To simplify the radical \( \sqrt{28x^4y^3} \), let's break it down step by step:

1. **Factor the constant and variables inside the radical**:
- \( 28 = 4 \times 7 \)
- \( x^4 \) is already a perfect square \( (x^2)^2 \)
- \( y^3 = y^2 \times y \), where \( y^2 \) is also a perfect square.

So we can rewrite the expression as:
\[
\sqrt{28x^4y^3} = \sqrt{4 \times 7 \times (x^2)^2 \times (y^2) \times y}
\]

2. **Apply the square root to each factor**:
\[
\sqrt{4} = 2, \quad \sqrt{(x^2)^2} = x^2, \quad \sqrt{y^2} = y
\]

Putting it all together gives:
\[
\sqrt{28x^4y^3} = 2x^2y\sqrt{7y}
\]

Thus, the simplified form of \( \sqrt{28x^4y^3} \) is:
\[
2x^2y\sqrt{7y}
\]

This matches the format of the choices you provided and it can be expressed as:
**2xy√7y**