Simplify -3i square root of -72

$- 3 i \sqrt{- 72}$

Step 1

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

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

Step 2

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

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

Step 3

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

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

Step 4

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

Factor $36$ out of $72$ .

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

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

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

Step 5

Pull terms out from under the radical.

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

Step 6

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

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

Step 7

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 $1$ .

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

Step 8

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

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

Step 9

Multiply $- 18$ by $- 1$ .

$18 \sqrt{2}$

Step 10

The result can be shown in multiple forms.

Exact Form:

$18 \sqrt{2}$

Decimal Form:

$25.45584412 \dots$

Simplify -3i square root of -72

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