SOLUTION
Given the question in the image, the following are the solution steps to answer the question.
STEP 1: Write the given expression
[tex]\sqrt{45n^5}[/tex]
STEP 2: Simplify the expression
[tex]\begin{gathered} \mathrm{Apply\:radical\:rule:\:}\sqrt{ab}=\sqrt{a}\sqrt{b},\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0 \\ \sqrt{45n^5}=\sqrt{45}\sqrt{n^5} \\ =\sqrt{45}\sqrt{n^5} \end{gathered}[/tex]
Simplify in units
[tex]\begin{gathered} \sqrt{n^5}=n^2\sqrt{n} \\ \sqrt{45}=\sqrt{9\cdot5}=\sqrt{9}\cdot\sqrt{5}=3\sqrt{5} \end{gathered}[/tex]
Combine the solutions to have:
[tex]=3\sqrt{5}n^2\sqrt{n}[/tex]
Hence, the answer is given as:
[tex]\begin{equation*} 3\sqrt{5}n^2\sqrt{n} \end{equation*}[/tex]
