Basic Math Examples

$\sqrt{- 20} - \sqrt{- 48}$

Step 1

Rewrite $- 20$ as $- 1 (20)$ .

$\sqrt{- 1 (20)} - \sqrt{- 48}$

Step 2

Rewrite $\sqrt{- 1 (20)}$ as $\sqrt{- 1} \cdot \sqrt{20}$ .

$\sqrt{- 1} \cdot \sqrt{20} - \sqrt{- 48}$

Step 3

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

$i \cdot \sqrt{20} - \sqrt{- 48}$

Step 4

Rewrite $20$ as $2^{2} \cdot 5$ .

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Step 4.1

Factor $4$ out of $20$ .

$i \cdot \sqrt{4 (5)} - \sqrt{- 48}$

Step 4.2

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

$i \cdot \sqrt{2^{2} \cdot 5} - \sqrt{- 48}$

Step 5

Pull terms out from under the radical.

$i \cdot (2 \sqrt{5}) - \sqrt{- 48}$

Step 6

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

$2 \cdot i \sqrt{5} - \sqrt{- 48}$

Step 7

Rewrite $- 48$ as $- 1 (48)$ .

$2 i \sqrt{5} - \sqrt{- 1 (48)}$

Step 8

Rewrite $\sqrt{- 1 (48)}$ as $\sqrt{- 1} \cdot \sqrt{48}$ .

$2 i \sqrt{5} - (\sqrt{- 1} \cdot \sqrt{48})$

Step 9

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

$2 i \sqrt{5} - (i \cdot \sqrt{48})$

Step 10

Rewrite $48$ as $4^{2} \cdot 3$ .

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Step 10.1

Factor $16$ out of $48$ .

$2 i \sqrt{5} - (i \cdot \sqrt{16 (3)})$

Step 10.2

Rewrite $16$ as $4^{2}$ .

$2 i \sqrt{5} - (i \cdot \sqrt{4^{2} \cdot 3})$

Step 11

Pull terms out from under the radical.

$2 i \sqrt{5} - (i \cdot (4 \sqrt{3}))$

Step 12

Move $4$ to the left of $i$ .

$2 i \sqrt{5} - (4 \cdot i \sqrt{3})$

Step 13

Multiply $4$ by $- 1$ .

$2 i \sqrt{5} - 4 i \sqrt{3}$