Finite Math Examples

$(8 + \sqrt{- 18}) - (5 + \sqrt{- 50})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 18$ as $- 1 (18)$ .

$8 + \sqrt{- 1 (18)} - (5 + \sqrt{- 50})$

Step 1.2

Rewrite $\sqrt{- 1 (18)}$ as $\sqrt{- 1} \cdot \sqrt{18}$ .

$8 + \sqrt{- 1} \cdot \sqrt{18} - (5 + \sqrt{- 50})$

Step 1.3

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

$8 + i \cdot \sqrt{18} - (5 + \sqrt{- 50})$

Step 1.4

Rewrite $18$ as $3^{2} \cdot 2$ .

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Step 1.4.1

Factor $9$ out of $18$ .

$8 + i \cdot \sqrt{9 (2)} - (5 + \sqrt{- 50})$

Step 1.4.2

Rewrite $9$ as $3^{2}$ .

$8 + i \cdot \sqrt{3^{2} \cdot 2} - (5 + \sqrt{- 50})$

Step 1.5

Pull terms out from under the radical.

$8 + i \cdot (3 \sqrt{2}) - (5 + \sqrt{- 50})$

Step 1.6

Move $3$ to the left of $i$ .

$8 + 3 \cdot i \sqrt{2} - (5 + \sqrt{- 50})$

Step 1.7

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

$8 + 3 i \sqrt{2} - (5 + \sqrt{- 1 (50)})$

Step 1.8

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

$8 + 3 i \sqrt{2} - (5 + \sqrt{- 1} \cdot \sqrt{50})$

Step 1.9

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

$8 + 3 i \sqrt{2} - (5 + i \cdot \sqrt{50})$

Step 1.10

Simplify each term.

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Step 1.10.1

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

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Step 1.10.1.1

Factor $25$ out of $50$ .

$8 + 3 i \sqrt{2} - (5 + i \cdot \sqrt{25 (2)})$

Step 1.10.1.2

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

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

Step 1.10.2

Pull terms out from under the radical.

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

Step 1.10.3

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

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

Step 1.11

Apply the distributive property.

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

Step 1.12

Multiply $- 1$ by $5$ .

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

Step 1.13

Multiply $5$ by $- 1$ .

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

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $5$ from $8$ .

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

Step 2.2

Subtract $5 i \sqrt{2}$ from $3 i \sqrt{2}$ .

$- 2 i \sqrt{2} + 3$

Step 2.3

Reorder $- 2 i \sqrt{2}$ and $3$ .

$3 - 2 i \sqrt{2}$