Simplify square root of 2i* square root of 6i

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

Multiply $\sqrt{2} i (\sqrt{6} i)$ .

Combine using the product rule for radicals.

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

Multiply $6$ by $2$ .

$\sqrt{12} i i$

Raise $i$ to the power of $1$ .

$\sqrt{12} (i^{1} i)$

Raise $i$ to the power of $1$ .

$\sqrt{12} (i^{1} i^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$\sqrt{12} i^{1 + 1}$

Add $1$ and $1$ .

$\sqrt{12} i^{2}$

Rewrite $12$ as $2^{2} \cdot 3$ .

Factor $4$ out of $12$ .

$\sqrt{4 (3)} i^{2}$

Rewrite $4$ as $2^{2}$ .

$\sqrt{2^{2} \cdot 3} i^{2}$

Pull terms out from under the radical.

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

Rewrite $i^{2}$ as $- 1$ .

$2 \sqrt{3} \cdot - 1$

Multiply $- 1$ by $2$ .

$- 2 \sqrt{3}$

The result can be shown in multiple forms.

Exact Form:

$- 2 \sqrt{3}$

Decimal Form:

$- 3.46410161 \dots$