Finite Math Examples

$- 3 + \sqrt{- 50} + (8 - \sqrt{- 98})$

Step 1

Remove parentheses.

$- 3 + \sqrt{- 50} + 8 - \sqrt{- 98}$

Step 2

Simplify each term.

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Step 2.1

Rewrite $- 50$ as $- 1 (50)$ .

$- 3 + \sqrt{- 1 (50)} + 8 - \sqrt{- 98}$

Step 2.2

Rewrite $\sqrt{- 1 (50)}$ as $\sqrt{- 1} \cdot \sqrt{50}$ .

$- 3 + \sqrt{- 1} \cdot \sqrt{50} + 8 - \sqrt{- 98}$

Step 2.3

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

$- 3 + i \cdot \sqrt{50} + 8 - \sqrt{- 98}$

Step 2.4

Rewrite $50$ as $5^{2} \cdot 2$ .

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Step 2.4.1

Factor $25$ out of $50$ .

$- 3 + i \cdot \sqrt{25 (2)} + 8 - \sqrt{- 98}$

Step 2.4.2

Rewrite $25$ as $5^{2}$ .

$- 3 + i \cdot \sqrt{5^{2} \cdot 2} + 8 - \sqrt{- 98}$

Step 2.5

Pull terms out from under the radical.

$- 3 + i \cdot (5 \sqrt{2}) + 8 - \sqrt{- 98}$

Step 2.6

Move $5$ to the left of $i$ .

$- 3 + 5 \cdot i \sqrt{2} + 8 - \sqrt{- 98}$

Step 2.7

Rewrite $- 98$ as $- 1 (98)$ .

$- 3 + 5 i \sqrt{2} + 8 - \sqrt{- 1 (98)}$

Step 2.8

Rewrite $\sqrt{- 1 (98)}$ as $\sqrt{- 1} \cdot \sqrt{98}$ .

$- 3 + 5 i \sqrt{2} + 8 - (\sqrt{- 1} \cdot \sqrt{98})$

Step 2.9

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

$- 3 + 5 i \sqrt{2} + 8 - (i \cdot \sqrt{98})$

Step 2.10

Rewrite $98$ as $7^{2} \cdot 2$ .

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Step 2.10.1

Factor $49$ out of $98$ .

$- 3 + 5 i \sqrt{2} + 8 - (i \cdot \sqrt{49 (2)})$

Step 2.10.2

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

$- 3 + 5 i \sqrt{2} + 8 - (i \cdot \sqrt{7^{2} \cdot 2})$

Step 2.11

Pull terms out from under the radical.

$- 3 + 5 i \sqrt{2} + 8 - (i \cdot (7 \sqrt{2}))$

Step 2.12

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

$- 3 + 5 i \sqrt{2} + 8 - (7 \cdot i \sqrt{2})$

Step 2.13

Multiply $7$ by $- 1$ .

$- 3 + 5 i \sqrt{2} + 8 - 7 i \sqrt{2}$

Step 3

Simplify by adding terms.

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Step 3.1

Add $- 3$ and $8$ .

$5 i \sqrt{2} + 5 - 7 i \sqrt{2}$

Step 3.2

Subtract $7 i \sqrt{2}$ from $5 i \sqrt{2}$ .

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

Step 3.3

Reorder $- 2 i \sqrt{2}$ and $5$ .

$5 - 2 i \sqrt{2}$