Simplify - square root of -49-5 square root of -9+3 cube root of -8

$- \sqrt{- 49} - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Step 1

Simplify each term.

Rewrite $- 49$ as $- 1 (49)$ .

$- \sqrt{- 1 (49)} - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$- (\sqrt{- 1} \cdot \sqrt{49}) - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

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

$- (i \cdot \sqrt{49}) - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Rewrite $49$ as $7^{2}$ .

$- (i \cdot \sqrt{7^{2}}) - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

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

$- (i \cdot 7) - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Move $7$ to the left of $i$ .

$- (7 \cdot i) - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Multiply $7$ by $- 1$ .

$- 7 i - 5 \sqrt{- 9} + 3 \sqrt[3]{- 8}$

Rewrite $- 9$ as $- 1 (9)$ .

$- 7 i - 5 \sqrt{- 1 (9)} + 3 \sqrt[3]{- 8}$

Rewrite $\sqrt{- 1 (9)}$ as $\sqrt{- 1} \cdot \sqrt{9}$ .

$- 7 i - 5 (\sqrt{- 1} \cdot \sqrt{9}) + 3 \sqrt[3]{- 8}$

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

$- 7 i - 5 (i \cdot \sqrt{9}) + 3 \sqrt[3]{- 8}$

Rewrite $9$ as $3^{2}$ .

$- 7 i - 5 (i \cdot \sqrt{3^{2}}) + 3 \sqrt[3]{- 8}$

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

$- 7 i - 5 (i \cdot 3) + 3 \sqrt[3]{- 8}$

Move $3$ to the left of $i$ .

$- 7 i - 5 (3 \cdot i) + 3 \sqrt[3]{- 8}$

Multiply $3$ by $- 5$ .

$- 7 i - 15 i + 3 \sqrt[3]{- 8}$

Rewrite $- 8$ as ${(- 2)}^{3}$ .

$- 7 i - 15 i + 3 \sqrt[3]{{(- 2)}^{3}}$

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

$- 7 i - 15 i + 3 \cdot - 2$

Multiply $3$ by $- 2$ .

$- 7 i - 15 i - 6$

Step 2

Simplify by adding terms.

Subtract $15 i$ from $- 7 i$ .

$- 22 i - 6$

Reorder $- 22 i$ and $- 6$ .

$- 6 - 22 i$