To simplify the algebraic expression [tex]\(\sqrt{45x^5}\)[/tex], let's follow a step-by-step process:
1. Factor the constants:
- Notice that 45 can be factored into [tex]\(9 \times 5\)[/tex].
- So, [tex]\(\sqrt{45x^5} = \sqrt{9 \times 5 \times x^5}\)[/tex].
2. Simplify the square root of the constant part:
- The square root of 9 is 3, so we can take the square root of 9 out of the radical.
- This gives us [tex]\(3 \sqrt{5x^5}\)[/tex].
3. Simplify the variable part under the square root:
- We can rewrite [tex]\(x^5\)[/tex] as [tex]\(x^4 \times x\)[/tex], since [tex]\(x^4 \times x = x^5\)[/tex].
- Hence, [tex]\(\sqrt{5x^5}\)[/tex] becomes [tex]\(\sqrt{5 x^4 x}\)[/tex].
4. Simplify the square root of the variable part:
- Since [tex]\(x^4\)[/tex] is a perfect square ([tex]\(x^4 = (x^2)^2\)[/tex]), we can take [tex]\(x^2\)[/tex] out of the radical.
- This gives us [tex]\(3 x^2 \sqrt{5 x}\)[/tex].
Putting it all together, the simplified form of the given expression is:
[tex]\[
3 x^2 \sqrt{5 x}
\][/tex]
Therefore, the correct answer is:
B. [tex]\(3 x^2 \sqrt{5 x}\)[/tex]
