Question

Can you help me simplify the radical expression and leave it in the radical form?

Answer 1

Given the question in the image, the following are the solution steps to answer the question.

STEP 1: Write the given expression

`√(45n^5)`

STEP 2: Simplify the expression

`\begin{gathered} \mathrm{Apply\:radical\:rule:\:}√(ab)=√(a)√(b),\:\quad \mathrm{\:assuming\:}a\ge 0,\:b\ge 0 \\ √(45n^5)=√(45)√(n^5) \\ =√(45)√(n^5) \end{gathered}`

Simplify in units

`\begin{gathered} √(n^5)=n^2√(n) \\ √(45)=√(9\cdot5)=√(9)\cdot√(5)=3√(5) \end{gathered}`

Combine the solutions to have:

`=3√(5)n^2√(n)`

Hence, the answer is given as:

`\begin{equation*} 3√(5)n^2√(n) \end{equation*}`