Question

divide.
\\(\frac{\sqrt{-12}}{\sqrt{-6}}\\)
\\(\frac{\sqrt{-12}}{\sqrt{-6}} = \square\\)
(simplify your answer. type an exact answer, using radicals and \\(i\\) as needed. use integers or fractions

Explanation:

Step1: Rewrite radicals with $i$

$\frac{\sqrt{-12}}{\sqrt{-6}} = \frac{i\sqrt{12}}{i\sqrt{6}}$

Step2: Cancel common factor $i$

$\frac{i\sqrt{12}}{i\sqrt{6}} = \frac{\sqrt{12}}{\sqrt{6}}$

Step3: Simplify the radical fraction

$\frac{\sqrt{12}}{\sqrt{6}} = \sqrt{\frac{12}{6}} = \sqrt{2}$

Answer:

$\sqrt{2}$