Algebra Examples

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

Step 1

Expand $(8 + 6 i) (6 i - 8)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $6$ by $8$ .

$\sqrt{48 i + 8 \cdot - 8 + 6 i (6 i) + 6 i \cdot - 8}$

Step 2.1.2

Multiply $8$ by $- 8$ .

$\sqrt{48 i - 64 + 6 i (6 i) + 6 i \cdot - 8}$

Step 2.1.3

Multiply $6 i (6 i)$ .

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Step 2.1.3.1

Multiply $6$ by $6$ .

$\sqrt{48 i - 64 + 36 i i + 6 i \cdot - 8}$

Step 2.1.3.2

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

$\sqrt{48 i - 64 + 36 (i^{1} i) + 6 i \cdot - 8}$

Step 2.1.3.3

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

$\sqrt{48 i - 64 + 36 (i^{1} i^{1}) + 6 i \cdot - 8}$

Step 2.1.3.4

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

$\sqrt{48 i - 64 + 36 i^{1 + 1} + 6 i \cdot - 8}$

Step 2.1.3.5

Add $1$ and $1$ .

$\sqrt{48 i - 64 + 36 i^{2} + 6 i \cdot - 8}$

Step 2.1.4

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

$\sqrt{48 i - 64 + 36 \cdot - 1 + 6 i \cdot - 8}$

Step 2.1.5

Multiply $36$ by $- 1$ .

$\sqrt{48 i - 64 - 36 + 6 i \cdot - 8}$

Step 2.1.6

Multiply $- 8$ by $6$ .

$\sqrt{48 i - 64 - 36 - 48 i}$

Step 2.2

Subtract $48 i$ from $48 i$ .

$\sqrt{0 - 64 - 36}$

Step 2.3

Subtract $64$ from $0$ .

$\sqrt{- 64 - 36}$

Step 2.4

Subtract $36$ from $- 64$ .

$\sqrt{- 100}$

Step 3

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

$\sqrt{- 1 (100)}$

Step 4

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

$\sqrt{- 1} \cdot \sqrt{100}$

Step 5

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

$i \cdot \sqrt{100}$

Step 6

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

$i \cdot \sqrt{10^{2}}$

Step 7

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

$i \cdot 10$

Step 8

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

$10 i$