Question

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

Answer 1

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