Answer:
[tex]\large\boxed{\sqrt{108}=6\sqrt3}[/tex]
Step-by-step explanation:
[tex]\sqrt{108}=\sqrt{4\cdot27}=\sqrt{4\cdot9\cdot3}\\\\\text{use}\ \sqrt{a\cdot b}=\sqrt{a}\cdot\sqrt{b}\\\\=\sqrt4\cdot\sqrt9\cdot\sqrt3=2\cdot3\cdot\sqrt3=6\sqrt3\\==========================\\\\\sqrt{108}=\sqrt{36\cdot3}=\sqrt{36}\cdot\sqrt3=6\sqrt3\\\\==========================\\\\\begin{array}{c|c}108&2\\54&2\\27&3\\9&3\\3&3\\1\end{array}\qquad108=2^2\cdot3^2\cdot3\\\\\sqrt{108}=\sqrt{2^2\cdot3^2\cdot3}=\sqrt{2^2}\cdot\sqrt{3^2}\cdot\sqrt3\\\\\text{use}\ \sqrt{a^2}=a\ \text{for}\ a\geq0\\\\=2\cdot3\cdot\sqrt3[/tex]
