Trigonometry Examples

$\sqrt{- 49} (8 - \sqrt{- 36})$

Step 1

Rewrite $- 49$ as $- 1 (49)$ .

$\sqrt{- 1 (49)} (8 - \sqrt{- 36})$

Step 2

Rewrite $\sqrt{- 1 (49)}$ as $\sqrt{- 1} \cdot \sqrt{49}$ .

$\sqrt{- 1} \cdot \sqrt{49} (8 - \sqrt{- 36})$

Step 3

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

$i \cdot \sqrt{49} (8 - \sqrt{- 36})$

Step 4

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

$i \cdot \sqrt{49} (8 - \sqrt{- 1 (36)})$

Step 5

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

$i \cdot \sqrt{49} (8 - (\sqrt{- 1} \cdot \sqrt{36}))$

Step 6

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

$i \cdot \sqrt{49} (8 - (i \cdot \sqrt{36}))$

Step 7

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

$i \cdot \sqrt{7^{2}} (8 - (i \cdot \sqrt{36}))$

Step 8

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

$i \cdot 7 (8 - (i \cdot \sqrt{36}))$

Step 9

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

$7 \cdot i (8 - (i \cdot \sqrt{36}))$

Step 10

Simplify each term.

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Step 10.1

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

$7 i (8 - (i \cdot \sqrt{6^{2}}))$

Step 10.2

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

$7 i (8 - (i \cdot 6))$

Step 10.3

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

$7 i (8 - (6 \cdot i))$

Step 10.4

Multiply $6$ by $- 1$ .

$7 i (8 - 6 i)$

Step 11

Simplify by multiplying through.

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Step 11.1

Apply the distributive property.

$7 i \cdot 8 + 7 i (- 6 i)$

Step 11.2

Multiply $8$ by $7$ .

$56 i + 7 i (- 6 i)$

Step 12

Multiply $7 i (- 6 i)$ .

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Step 12.1

Multiply $- 6$ by $7$ .

$56 i - 42 i i$

Step 12.2

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

$56 i - 42 (i^{1} i)$

Step 12.3

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

$56 i - 42 (i^{1} i^{1})$

Step 12.4

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

$56 i - 42 i^{1 + 1}$

Step 12.5

Add $1$ and $1$ .

$56 i - 42 i^{2}$

Step 13

Simplify each term.

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Step 13.1

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

$56 i - 42 \cdot - 1$

Step 13.2

Multiply $- 42$ by $- 1$ .

$56 i + 42$

Step 14

Reorder $56 i$ and $42$ .

$42 + 56 i$