Basic Math Examples

$\sqrt{112} - \sqrt{48} + (4 \sqrt{7} + \sqrt{- 147})$

Step 1

Remove parentheses.

$\sqrt{112} - \sqrt{48} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $112$ as $4^{2} \cdot 7$ .

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Step 2.1.1

Factor $16$ out of $112$ .

$\sqrt{16 (7)} - \sqrt{48} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.1.2

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

$\sqrt{4^{2} \cdot 7} - \sqrt{48} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.2

Pull terms out from under the radical.

$4 \sqrt{7} - \sqrt{48} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.3

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

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Step 2.3.1

Factor $16$ out of $48$ .

$4 \sqrt{7} - \sqrt{16 (3)} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.3.2

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

$4 \sqrt{7} - \sqrt{4^{2} \cdot 3} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.4

Pull terms out from under the radical.

$4 \sqrt{7} - (4 \sqrt{3}) + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.5

Multiply $4$ by $- 1$ .

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + \sqrt{- 147}$

Step 2.6

Rewrite $- 147$ as $- 1 (147)$ .

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + \sqrt{- 1 (147)}$

Step 2.7

Rewrite $\sqrt{- 1 (147)}$ as $\sqrt{- 1} \cdot \sqrt{147}$ .

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + \sqrt{- 1} \cdot \sqrt{147}$

Step 2.8

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

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + i \cdot \sqrt{147}$

Step 2.9

Rewrite $147$ as $7^{2} \cdot 3$ .

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Step 2.9.1

Factor $49$ out of $147$ .

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + i \cdot \sqrt{49 (3)}$

Step 2.9.2

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

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + i \cdot \sqrt{7^{2} \cdot 3}$

Step 2.10

Pull terms out from under the radical.

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + i \cdot (7 \sqrt{3})$

Step 2.11

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

$4 \sqrt{7} - 4 \sqrt{3} + 4 \sqrt{7} + 7 i \sqrt{3}$

Step 3

Add $4 \sqrt{7}$ and $4 \sqrt{7}$ .

$8 \sqrt{7} - 4 \sqrt{3} + 7 i \sqrt{3}$