Question

What is the square root of 216?

Answer 1

$\sqrt{216}=\sqrt{36\cdot6}=\sqrt{36}\cdot\sqrt6=6\sqrt6$


$216|2\\108|2\\.\ 54|2\\.\ 27|3\\.\ \ 9|3\\.\ \ 3|3\\.\ \ 1\\\\216=2^2\cdot3^2\cdot2\cdot3\\\\\sqrt{216}=\sqrt{2^2\cdot3^2\cdot2\cdot3}=\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt6=2\cdot3\cdot\sqrt6=6\sqrt6$