Question

What is the simplified form of the square root of 48n^9

Answer 1

`\bf √(48n^9)\qquad\begin{cases} 48=2\cdot 2\cdot 2\cdot 2\cdot 3\\ \qquad 2^2\cdot 2^2\cdot 3\\ \qquad (2^2)^2\cdot 3\\ n^9=n^(8+1)\\ \qquad n^8\cdot n^1\\ \qquad n^(4\cdot 2)\cdot n\\ \qquad (n^4)^2\cdot n \end{cases}\implies √((2^2)^2\cdot 3\cdot (n^4)^2\cdot n) \\\\\\ 2^2n^4√(3n)\implies 4n^4√(3n)`