Simplify ( square root of 18)/(2i square root of 6)

$\frac{\sqrt{18}}{2 i \sqrt{6}}$

Combine $\sqrt{18}$ and $\sqrt{6}$ into a single radical.

$\frac{\sqrt{\frac{18}{6}}}{2 i}$

Cancel the common factor of $18$ and $6$ .

Factor $6$ out of $18$ .

$\frac{\sqrt{\frac{6 \cdot 3}{6}}}{2 i}$

Cancel the common factors.

Factor $6$ out of $6$ .

$\frac{\sqrt{\frac{6 \cdot 3}{6 (1)}}}{2 i}$

Cancel the common factor.

$\frac{\sqrt{\frac{6 \cdot 3}{6 \cdot 1}}}{2 i}$

Rewrite the expression.

$\frac{\sqrt{\frac{3}{1}}}{2 i}$

Divide $3$ by $1$ .

$\frac{\sqrt{3}}{2 i}$