Simplify 3i square root of -72

$3 i \sqrt{- 72}$

Rewrite $- 72$ as $- 1 (72)$ .

$3 i \sqrt{- 1 (72)}$

Rewrite $\sqrt{- 1 (72)}$ as $\sqrt{- 1} \cdot \sqrt{72}$ .

$3 i (\sqrt{- 1} \cdot \sqrt{72})$

Rewrite $\sqrt{- 1}$ as $i$ .

$3 i (i \cdot \sqrt{72})$

Rewrite $72$ as $6^{2} \cdot 2$ .

Factor $36$ out of $72$ .

$3 i (i \cdot \sqrt{36 (2)})$

Rewrite $36$ as $6^{2}$ .

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

Pull terms out from under the radical.

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

Move $6$ to the left of $i$ .

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

Multiply $3 i (6 i \sqrt{2})$ .

Multiply $6$ by $3$ .

$18 i (i \sqrt{2})$

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

$18 (i^{1} i) \sqrt{2}$

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

$18 (i^{1} i^{1}) \sqrt{2}$

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

$18 i^{1 + 1} \sqrt{2}$

Add $1$ and $1$ .

$18 i^{2} \sqrt{2}$

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

$18 \cdot - 1 \sqrt{2}$

Multiply $18$ by $- 1$ .

$- 18 \sqrt{2}$

The result can be shown in multiple forms.

Exact Form:

$- 18 \sqrt{2}$

Decimal Form:

$- 25.45584412 \dots$