Question

Express in simplest radical form.
square root of, 2, x, to the power 9 , end square root
2x
9

​

Answer
Multiple Choice Answers
square root of, 2, x, to the power 9 , end square root
2x
9

​

x, to the power 5 , square root of, 2, x, end square rootx
5

2x
​

2, x, to the power 42x
4

x, to the power 4 , square root of, 2, x, end square rootx
4

2x
​

Answer 1

To simplify \(\sqrt{2x^9}\), we can break it down as follows:

1. Separate the square root into components:
\[
\sqrt{2x^9} = \sqrt{2} \cdot \sqrt{x^9}
\]

2. Simplify \(\sqrt{x^9}\):
\[
\sqrt{x^9} = \sqrt{x^{8} \cdot x^1} = \sqrt{x^{8}} \cdot \sqrt{x} = x^4 \cdot \sqrt{x}
\]

3. Rewrite the expression:
\[
\sqrt{2x^9} = \sqrt{2} \cdot x^4 \cdot \sqrt{x} = x^4 \sqrt{2x}
\]

So, the simplified form of \(\sqrt{2x^9}\) is:
\[
x^4 \sqrt{2x}
\]

Now let's check the provided multiple choice answers to see which corresponds to our simplification:
- \( x^5 \sqrt{2x} \)
- \( 2x \)
- \( 2x^4 \sqrt{2x} \)
- \( x^4 \sqrt{2x} \)

The correct answer is:
\[
x^4 \sqrt{2x}
\]