Algebra Examples

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

Step 1

Simplify each term.

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Step 1.1

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

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

Step 1.2

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

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

Step 1.3

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

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

Step 1.4

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

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

Step 1.5

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

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

Step 1.6

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

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

Step 1.7

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

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

Step 1.8

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

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

Step 1.9

Multiply $4$ by $10$ .

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

Step 1.10

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

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

Step 1.11

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

$7 i + 40 + 5 \cdot 9$

Step 1.12

Multiply $5$ by $9$ .

$7 i + 40 + 45$

Step 2

Simplify the expression.

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Step 2.1

Add $40$ and $45$ .

$7 i + 85$

Step 2.2

Reorder $7 i$ and $85$ .

$85 + 7 i$