Simplify 2 square root of 81+4 square root of -64+ cube root of -64+ square root of -100

$2 \sqrt{81} + 4 \sqrt{- 64} + \sqrt[3]{- 64} + \sqrt{- 100}$

Step 1

Simplify each term.

Rewrite $81$ as $9^{2}$ .

$2 \sqrt{9^{2}} + 4 \sqrt{- 64} + \sqrt[3]{- 64} + \sqrt{- 100}$

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

$2 \cdot 9 + 4 \sqrt{- 64} + \sqrt[3]{- 64} + \sqrt{- 100}$

Multiply $2$ by $9$ .

$18 + 4 \sqrt{- 64} + \sqrt[3]{- 64} + \sqrt{- 100}$

Rewrite $- 64$ as $- 1 (64)$ .

$18 + 4 \sqrt{- 1 (64)} + \sqrt[3]{- 64} + \sqrt{- 100}$

Rewrite $\sqrt{- 1 (64)}$ as $\sqrt{- 1} \cdot \sqrt{64}$ .

$18 + 4 (\sqrt{- 1} \cdot \sqrt{64}) + \sqrt[3]{- 64} + \sqrt{- 100}$

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

$18 + 4 (i \cdot \sqrt{64}) + \sqrt[3]{- 64} + \sqrt{- 100}$

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

$18 + 4 (i \cdot \sqrt{8^{2}}) + \sqrt[3]{- 64} + \sqrt{- 100}$

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

$18 + 4 (i \cdot 8) + \sqrt[3]{- 64} + \sqrt{- 100}$

Move $8$ to the left of $i$ .

$18 + 4 (8 \cdot i) + \sqrt[3]{- 64} + \sqrt{- 100}$

Multiply $8$ by $4$ .

$18 + 32 i + \sqrt[3]{- 64} + \sqrt{- 100}$

Rewrite $- 64$ as ${(- 4)}^{3}$ .

$18 + 32 i + \sqrt[3]{{(- 4)}^{3}} + \sqrt{- 100}$

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

$18 + 32 i - 4 + \sqrt{- 100}$

Rewrite $- 100$ as $- 1 (100)$ .

$18 + 32 i - 4 + \sqrt{- 1 (100)}$

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$18 + 32 i - 4 + \sqrt{- 1} \cdot \sqrt{100}$

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

$18 + 32 i - 4 + i \cdot \sqrt{100}$

Rewrite $100$ as $10^{2}$ .

$18 + 32 i - 4 + i \cdot \sqrt{10^{2}}$

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

$18 + 32 i - 4 + i \cdot 10$

Move $10$ to the left of $i$ .

$18 + 32 i - 4 + 10 i$

Step 2

Simplify by adding terms.

Subtract $4$ from $18$ .

$14 + 32 i + 10 i$

Add $32 i$ and $10 i$ .

$14 + 42 i$