Finite Math Examples

$(8 + \sqrt{- 144}) \cdot (\sqrt{- 196} - \sqrt{- 225})$

Step 1

Rewrite $- 144$ as $- 1 (144)$ .

$(8 + \sqrt{- 1 (144)}) \cdot (\sqrt{- 196} - \sqrt{- 225})$

Step 2

Rewrite $\sqrt{- 1 (144)}$ as $\sqrt{- 1} \cdot \sqrt{144}$ .

$(8 + \sqrt{- 1} \cdot \sqrt{144}) \cdot (\sqrt{- 196} - \sqrt{- 225})$

Step 3

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

$(8 + i \cdot \sqrt{144}) \cdot (\sqrt{- 196} - \sqrt{- 225})$

Step 4

Rewrite $- 196$ as $- 1 (196)$ .

$(8 + i \cdot \sqrt{144}) \cdot (\sqrt{- 1 (196)} - \sqrt{- 225})$

Step 5

Rewrite $\sqrt{- 1 (196)}$ as $\sqrt{- 1} \cdot \sqrt{196}$ .

$(8 + i \cdot \sqrt{144}) \cdot (\sqrt{- 1} \cdot \sqrt{196} - \sqrt{- 225})$

Step 6

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

$(8 + i \cdot \sqrt{144}) \cdot (i \cdot \sqrt{196} - \sqrt{- 225})$

Step 7

Rewrite $- 225$ as $- 1 (225)$ .

$(8 + i \cdot \sqrt{144}) \cdot (i \cdot \sqrt{196} - \sqrt{- 1 (225)})$

Step 8

Rewrite $\sqrt{- 1 (225)}$ as $\sqrt{- 1} \cdot \sqrt{225}$ .

$(8 + i \cdot \sqrt{144}) \cdot (i \cdot \sqrt{196} - (\sqrt{- 1} \cdot \sqrt{225}))$

Step 9

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

$(8 + i \cdot \sqrt{144}) \cdot (i \cdot \sqrt{196} - (i \cdot \sqrt{225}))$

Step 10

Simplify each term.

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Step 10.1

Rewrite $144$ as $12^{2}$ .

$(8 + i \cdot \sqrt{12^{2}}) \cdot (i \cdot \sqrt{196} - (i \cdot \sqrt{225}))$

Step 10.2

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

$(8 + i \cdot 12) \cdot (i \cdot \sqrt{196} - (i \cdot \sqrt{225}))$

Step 10.3

Move $12$ to the left of $i$ .

$(8 + 12 i) \cdot (i \cdot \sqrt{196} - (i \cdot \sqrt{225}))$

Step 11

Simplify each term.

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Step 11.1

Rewrite $196$ as $14^{2}$ .

$(8 + 12 i) \cdot (i \cdot \sqrt{14^{2}} - (i \cdot \sqrt{225}))$

Step 11.2

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

$(8 + 12 i) \cdot (i \cdot 14 - (i \cdot \sqrt{225}))$

Step 11.3

Move $14$ to the left of $i$ .

$(8 + 12 i) \cdot (14 \cdot i - (i \cdot \sqrt{225}))$

Step 11.4

Rewrite $225$ as $15^{2}$ .

$(8 + 12 i) \cdot (14 i - (i \cdot \sqrt{15^{2}}))$

Step 11.5

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

$(8 + 12 i) \cdot (14 i - (i \cdot 15))$

Step 11.6

Move $15$ to the left of $i$ .

$(8 + 12 i) \cdot (14 i - (15 \cdot i))$

Step 11.7

Multiply $15$ by $- 1$ .

$(8 + 12 i) \cdot (14 i - 15 i)$

Step 12

Simplify terms.

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Step 12.1

Subtract $15 i$ from $14 i$ .

$(8 + 12 i) \cdot (- i)$

Step 12.2

Apply the distributive property.

$8 (- i) + 12 i (- i)$

Step 12.3

Multiply $- 1$ by $8$ .

$- 8 i + 12 i (- i)$

Step 13

Multiply $12 i (- i)$ .

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Step 13.1

Multiply $- 1$ by $12$ .

$- 8 i - 12 i i$

Step 13.2

Raise $i$ to the power of $1$ .

$- 8 i - 12 (i^{1} i)$

Step 13.3

Raise $i$ to the power of $1$ .

$- 8 i - 12 (i^{1} i^{1})$

Step 13.4

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$- 8 i - 12 i^{1 + 1}$

Step 13.5

Add $1$ and $1$ .

$- 8 i - 12 i^{2}$

Step 14

Simplify each term.

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Step 14.1

Rewrite $i^{2}$ as $- 1$ .

$- 8 i - 12 \cdot - 1$

Step 14.2

Multiply $- 12$ by $- 1$ .

$- 8 i + 12$

Step 15

Reorder $- 8 i$ and $12$ .

$12 - 8 i$