To simplify the expression [tex]\(\sqrt{50 x^9}\)[/tex], we can follow these steps:
1. Factor the expression inside the square root:
[tex]\[ 50 x^9 = 25 \times 2 \times x^8 \times x \][/tex]
Here, we have split [tex]\(50\)[/tex] into [tex]\(25 \times 2\)[/tex] and [tex]\(x^9\)[/tex] into [tex]\(x^8 \times x\)[/tex].
2. Simplify the square roots of the factored parts:
[tex]\[ \sqrt{50 x^9} = \sqrt{25 \times 2 \times x^8 \times x} \][/tex]
3. Use the property [tex]\(\sqrt{a \times b} = \sqrt{a} \times \sqrt{b}\)[/tex]:
[tex]\[ \sqrt{50 x^9} = \sqrt{25} \times \sqrt{2} \times \sqrt{x^8} \times \sqrt{x} \][/tex]
4. Simplify the square roots of the perfect squares:
[tex]\[ \sqrt{25} = 5 \][/tex]
[tex]\[ \sqrt{x^8} = x^4 \][/tex]
Thus:
[tex]\[ \sqrt{50 x^9} = 5 \times \sqrt{2} \times x^4 \times \sqrt{x} \][/tex]
5. Combine the simplified parts:
[tex]\[ \sqrt{50 x^9} = 5 x^4 \sqrt{2} \sqrt{x} \][/tex]
6. Merge the remaining square roots:
[tex]\[ \sqrt{2} \times \sqrt{x} = \sqrt{2x} \][/tex]
Therefore:
[tex]\[ \sqrt{50 x^9} = 5 x^4 \sqrt{2x} \][/tex]
Thus, the simplest form of [tex]\(\sqrt{50 x^9}\)[/tex] is [tex]\(5 x^4 \sqrt{2 x}\)[/tex].
Therefore, the correct answer is:
[tex]\[ \boxed{B. 5 x^4 \sqrt{2 x}} \][/tex]
