Basic Math Examples

$\sqrt{49} + \sqrt{- 49}$

Step 1

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

$\sqrt{7^{2}} + \sqrt{- 49}$

Step 2

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

$7 + \sqrt{- 49}$

Step 3

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

$7 + \sqrt{- 1 (49)}$

Step 4

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

$7 + \sqrt{- 1} \cdot \sqrt{49}$

Step 5

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

$7 + i \cdot \sqrt{49}$

Step 6

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

$7 + i \cdot \sqrt{7^{2}}$

Step 7

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

$7 + i \cdot 7$

Step 8

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

$7 + 7 i$