Simplify square root of -49+4 cube root of 1000+5 square root of 81

$\sqrt{- 49} + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

Simplify each term.

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

$\sqrt{- 1 (49)} + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

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

$\sqrt{- 1} \cdot \sqrt{49} + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

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

$i \cdot \sqrt{49} + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

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

$i \cdot \sqrt{7^{2}} + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

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

$i \cdot 7 + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

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

$7 \cdot i + 4 \sqrt[3]{1000} + 5 \sqrt{81}$

Rewrite $1000$ as $10^{3}$ .

$7 i + 4 \sqrt[3]{10^{3}} + 5 \sqrt{81}$

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

$7 i + 4 \cdot 10 + 5 \sqrt{81}$

Multiply $4$ by $10$ .

$7 i + 40 + 5 \sqrt{81}$

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

$7 i + 40 + 5 \sqrt{9^{2}}$

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

$7 i + 40 + 5 \cdot 9$

Multiply $5$ by $9$ .

$7 i + 40 + 45$

Simplify the expression.

Add $40$ and $45$ .

$7 i + 85$

Reorder $7 i$ and $85$ .

$85 + 7 i$