Basic Math Examples

$(6 + \sqrt{- 100}) - (8 + \sqrt{- 81})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 100$ as $- 1 (100)$ .

$6 + \sqrt{- 1 (100)} - (8 + \sqrt{- 81})$

Step 1.2

Rewrite $\sqrt{- 1 (100)}$ as $\sqrt{- 1} \cdot \sqrt{100}$ .

$6 + \sqrt{- 1} \cdot \sqrt{100} - (8 + \sqrt{- 81})$

Step 1.3

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

$6 + i \cdot \sqrt{100} - (8 + \sqrt{- 81})$

Step 1.4

Rewrite $100$ as $10^{2}$ .

$6 + i \cdot \sqrt{10^{2}} - (8 + \sqrt{- 81})$

Step 1.5

Pull terms out from under the radical, assuming positive real numbers.

$6 + i \cdot 10 - (8 + \sqrt{- 81})$

Step 1.6

Move $10$ to the left of $i$ .

$6 + 10 \cdot i - (8 + \sqrt{- 81})$

Step 1.7

Rewrite $- 81$ as $- 1 (81)$ .

$6 + 10 i - (8 + \sqrt{- 1 (81)})$

Step 1.8

Rewrite $\sqrt{- 1 (81)}$ as $\sqrt{- 1} \cdot \sqrt{81}$ .

$6 + 10 i - (8 + \sqrt{- 1} \cdot \sqrt{81})$

Step 1.9

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

$6 + 10 i - (8 + i \cdot \sqrt{81})$

Step 1.10

Simplify each term.

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Step 1.10.1

Rewrite $81$ as $9^{2}$ .

$6 + 10 i - (8 + i \cdot \sqrt{9^{2}})$

Step 1.10.2

Pull terms out from under the radical, assuming positive real numbers.

$6 + 10 i - (8 + i \cdot 9)$

Step 1.10.3

Move $9$ to the left of $i$ .

$6 + 10 i - (8 + 9 i)$

Step 1.11

Apply the distributive property.

$6 + 10 i - 1 \cdot 8 - (9 i)$

Step 1.12

Multiply $- 1$ by $8$ .

$6 + 10 i - 8 - (9 i)$

Step 1.13

Multiply $9$ by $- 1$ .

$6 + 10 i - 8 - 9 i$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8$ from $6$ .

$- 2 + 10 i - 9 i$

Step 2.2

Subtract $9 i$ from $10 i$ .

$- 2 + i$