Question

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

Answer 1

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

1. **Factor inside the square root:**
\[
28 = 4 \times 7
\]
So, we rewrite the expression as:
\[
\sqrt{28x^4y^3} = \sqrt{4 \times 7 \times x^4 \times y^3}
\]

2. **Break down the square root:**
By using the property \(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\), we can split the square root:
\[
\sqrt{28x^4y^3} = \sqrt{4} \times \sqrt{7} \times \sqrt{x^4} \times \sqrt{y^3}
\]

3. **Calculate the square roots:**
- \(\sqrt{4} = 2\)
- \(\sqrt{x^4} = x^2\) (since \(\sqrt{x^m} = x^{m/2}\), and \(4/2 = 2\))
- For \(y^3\), we can express \(\sqrt{y^3} = \sqrt{y^2 \times y} = \sqrt{y^2} \times \sqrt{y} = y \sqrt{y}\)

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

4. **Combine the terms:**
Now, we can combine all the simplifications together:
\[
= 2x^2y \sqrt{7y}
\]

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

Therefore, the correct response is: **\(2x^2y\sqrt{7y}\)**.