Basic Math Examples

$- 2 + \sqrt{- 8} + (5 - \sqrt{- 52})$

Step 1

Remove parentheses.

$- 2 + \sqrt{- 8} + 5 - \sqrt{- 52}$

Step 2

Simplify each term.

Tap for more steps...

Step 2.1

Rewrite $- 8$ as $- 1 (8)$ .

$- 2 + \sqrt{- 1 (8)} + 5 - \sqrt{- 52}$

Step 2.2

Rewrite $\sqrt{- 1 (8)}$ as $\sqrt{- 1} \cdot \sqrt{8}$ .

$- 2 + \sqrt{- 1} \cdot \sqrt{8} + 5 - \sqrt{- 52}$

Step 2.3

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

$- 2 + i \cdot \sqrt{8} + 5 - \sqrt{- 52}$

Step 2.4

Rewrite $8$ as $2^{2} \cdot 2$ .

Tap for more steps...

Step 2.4.1

Factor $4$ out of $8$ .

$- 2 + i \cdot \sqrt{4 (2)} + 5 - \sqrt{- 52}$

Step 2.4.2

Rewrite $4$ as $2^{2}$ .

$- 2 + i \cdot \sqrt{2^{2} \cdot 2} + 5 - \sqrt{- 52}$

Step 2.5

Pull terms out from under the radical.

$- 2 + i \cdot (2 \sqrt{2}) + 5 - \sqrt{- 52}$

Step 2.6

Move $2$ to the left of $i$ .

$- 2 + 2 \cdot i \sqrt{2} + 5 - \sqrt{- 52}$

Step 2.7

Rewrite $- 52$ as $- 1 (52)$ .

$- 2 + 2 i \sqrt{2} + 5 - \sqrt{- 1 (52)}$

Step 2.8

Rewrite $\sqrt{- 1 (52)}$ as $\sqrt{- 1} \cdot \sqrt{52}$ .

$- 2 + 2 i \sqrt{2} + 5 - (\sqrt{- 1} \cdot \sqrt{52})$

Step 2.9

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

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot \sqrt{52})$

Step 2.10

Rewrite $52$ as $2^{2} \cdot 13$ .

Tap for more steps...

Step 2.10.1

Factor $4$ out of $52$ .

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot \sqrt{4 (13)})$

Step 2.10.2

Rewrite $4$ as $2^{2}$ .

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot \sqrt{2^{2} \cdot 13})$

Step 2.11

Pull terms out from under the radical.

$- 2 + 2 i \sqrt{2} + 5 - (i \cdot (2 \sqrt{13}))$

Step 2.12

Move $2$ to the left of $i$ .

$- 2 + 2 i \sqrt{2} + 5 - (2 \cdot i \sqrt{13})$

Step 2.13

Multiply $2$ by $- 1$ .

$- 2 + 2 i \sqrt{2} + 5 - 2 i \sqrt{13}$

Step 3

Simplify the expression.

Tap for more steps...

Step 3.1

Add $- 2$ and $5$ .

$2 i \sqrt{2} + 3 - 2 i \sqrt{13}$

Step 3.2

Reorder $2 i \sqrt{2}$ and $3$ .

$3 + 2 i \sqrt{2} - 2 i \sqrt{13}$