Basic Math Examples

$(13 - \sqrt{- 121}) - (- 4 + \sqrt{- 36})$

Step 1

Simplify each term.

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Step 1.1

Rewrite $- 121$ as $- 1 (121)$ .

$13 - \sqrt{- 1 (121)} - (- 4 + \sqrt{- 36})$

Step 1.2

Rewrite $\sqrt{- 1 (121)}$ as $\sqrt{- 1} \cdot \sqrt{121}$ .

$13 - (\sqrt{- 1} \cdot \sqrt{121}) - (- 4 + \sqrt{- 36})$

Step 1.3

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

$13 - (i \cdot \sqrt{121}) - (- 4 + \sqrt{- 36})$

Step 1.4

Rewrite $121$ as $11^{2}$ .

$13 - (i \cdot \sqrt{11^{2}}) - (- 4 + \sqrt{- 36})$

Step 1.5

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

$13 - (i \cdot 11) - (- 4 + \sqrt{- 36})$

Step 1.6

Move $11$ to the left of $i$ .

$13 - (11 \cdot i) - (- 4 + \sqrt{- 36})$

Step 1.7

Multiply $11$ by $- 1$ .

$13 - 11 i - (- 4 + \sqrt{- 36})$

Step 1.8

Rewrite $- 36$ as $- 1 (36)$ .

$13 - 11 i - (- 4 + \sqrt{- 1 (36)})$

Step 1.9

Rewrite $\sqrt{- 1 (36)}$ as $\sqrt{- 1} \cdot \sqrt{36}$ .

$13 - 11 i - (- 4 + \sqrt{- 1} \cdot \sqrt{36})$

Step 1.10

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

$13 - 11 i - (- 4 + i \cdot \sqrt{36})$

Step 1.11

Simplify each term.

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Step 1.11.1

Rewrite $36$ as $6^{2}$ .

$13 - 11 i - (- 4 + i \cdot \sqrt{6^{2}})$

Step 1.11.2

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

$13 - 11 i - (- 4 + i \cdot 6)$

Step 1.11.3

Move $6$ to the left of $i$ .

$13 - 11 i - (- 4 + 6 i)$

Step 1.12

Apply the distributive property.

$13 - 11 i - - 4 - (6 i)$

Step 1.13

Multiply $- 1$ by $- 4$ .

$13 - 11 i + 4 - (6 i)$

Step 1.14

Multiply $6$ by $- 1$ .

$13 - 11 i + 4 - 6 i$

Step 2

Simplify by adding terms.

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Step 2.1

Add $13$ and $4$ .

$17 - 11 i - 6 i$

Step 2.2

Subtract $6 i$ from $- 11 i$ .

$17 - 17 i$