Basic Math Examples

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

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

Step 1

Rewrite

- 20

$- 20$ as

- 1 (20)

$- 1 (20)$ .

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

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

Step 2

Rewrite

\sqrt{- 1 (20)}

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

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

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

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

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

Step 3

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

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

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

Step 4

Rewrite

20

$20$ as

2^{2} \cdot 5

$2^{2} \cdot 5$ .

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Step 4.1

Factor

4

$4$ out of

20

$20$ .

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

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

Step 4.2

Rewrite

4

$4$ as

2^{2}

$2^{2}$ .

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

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

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

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

Step 5

Pull terms out from under the radical.

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

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

Step 6

Move

2

$2$ to the left of

i

$i$ .

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

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

Step 7

Rewrite

- 48

$- 48$ as

- 1 (48)

$- 1 (48)$ .

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

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

Step 8

Rewrite

\sqrt{- 1 (48)}

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

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

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

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

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

Step 9

Rewrite

\sqrt{- 1}

$\sqrt{- 1}$ as

i

$i$ .

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

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

Step 10

Rewrite

48

$48$ as

4^{2} \cdot 3

$4^{2} \cdot 3$ .

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Step 10.1

Factor

16

$16$ out of

48

$48$ .

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

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

Step 10.2

Rewrite

16

$16$ as

4^{2}

$4^{2}$ .

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

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

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

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

Step 11

Pull terms out from under the radical.

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

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

Step 12

Move

4

$4$ to the left of

i

$i$ .

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

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

Step 13

Multiply

4

$4$ by

- 1

$- 1$ .

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

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

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$