Simplify square root of 144- square root of -72- square root of 64- square root of -72

$\sqrt{144} - \sqrt{- 72} - \sqrt{64} - \sqrt{- 72}$

Step 1

Simplify each term.

Rewrite $144$ as $12^{2}$ .

$\sqrt{12^{2}} - \sqrt{- 72} - \sqrt{64} - \sqrt{- 72}$

Pull terms out from under the radical, assuming positive real numbers.

$12 - \sqrt{- 72} - \sqrt{64} - \sqrt{- 72}$

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

$12 - \sqrt{- 1 (72)} - \sqrt{64} - \sqrt{- 72}$

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

$12 - (\sqrt{- 1} \cdot \sqrt{72}) - \sqrt{64} - \sqrt{- 72}$

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

$12 - (i \cdot \sqrt{72}) - \sqrt{64} - \sqrt{- 72}$

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

Factor $36$ out of $72$ .

$12 - (i \cdot \sqrt{36 (2)}) - \sqrt{64} - \sqrt{- 72}$

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

$12 - (i \cdot \sqrt{6^{2} \cdot 2}) - \sqrt{64} - \sqrt{- 72}$

Pull terms out from under the radical.

$12 - (i \cdot (6 \sqrt{2})) - \sqrt{64} - \sqrt{- 72}$

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

$12 - (6 \cdot i \sqrt{2}) - \sqrt{64} - \sqrt{- 72}$

Multiply $6$ by $- 1$ .

$12 - 6 (i \sqrt{2}) - \sqrt{64} - \sqrt{- 72}$

Rewrite $64$ as $8^{2}$ .

$12 - 6 i \sqrt{2} - \sqrt{8^{2}} - \sqrt{- 72}$

Pull terms out from under the radical, assuming positive real numbers.

$12 - 6 i \sqrt{2} - 1 \cdot 8 - \sqrt{- 72}$

Multiply $- 1$ by $8$ .

$12 - 6 i \sqrt{2} - 8 - \sqrt{- 72}$

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

$12 - 6 i \sqrt{2} - 8 - \sqrt{- 1 (72)}$

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

$12 - 6 i \sqrt{2} - 8 - (\sqrt{- 1} \cdot \sqrt{72})$

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

$12 - 6 i \sqrt{2} - 8 - (i \cdot \sqrt{72})$

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

Factor $36$ out of $72$ .

$12 - 6 i \sqrt{2} - 8 - (i \cdot \sqrt{36 (2)})$

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

$12 - 6 i \sqrt{2} - 8 - (i \cdot \sqrt{6^{2} \cdot 2})$

Pull terms out from under the radical.

$12 - 6 i \sqrt{2} - 8 - (i \cdot (6 \sqrt{2}))$

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

$12 - 6 i \sqrt{2} - 8 - (6 \cdot i \sqrt{2})$

Multiply $6$ by $- 1$ .

$12 - 6 i \sqrt{2} - 8 - 6 i \sqrt{2}$

Step 2

Simplify by adding terms.

Subtract $8$ from $12$ .

$- 6 i \sqrt{2} + 4 - 6 i \sqrt{2}$

Subtract $6 i \sqrt{2}$ from $- 6 i \sqrt{2}$ .

$- 12 i \sqrt{2} + 4$

Reorder $- 12 i \sqrt{2}$ and $4$ .

$4 - 12 i \sqrt{2}$

Simplify square root of 144- square root of -72- square root of 64- square root of -72

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