Algebra Examples

$i \sqrt{8} \cdot i \sqrt{2}$

Step 1

Rewrite $8$ as $2^{2} \cdot 2$ .

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Step 1.1

Factor $4$ out of $8$ .

$i \sqrt{4 (2)} \cdot (i \sqrt{2})$

Step 1.2

Rewrite $4$ as $2^{2}$ .

$i \sqrt{2^{2} \cdot 2} \cdot (i \sqrt{2})$

Step 2

Pull terms out from under the radical.

$i (2 \sqrt{2}) \cdot (i \sqrt{2})$

Step 3

Move $2$ to the left of $i$ .

$2 \cdot i \sqrt{2} \cdot (i \sqrt{2})$

Step 4

Multiply $2 i \sqrt{2} (i \sqrt{2})$ .

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Step 4.1

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

$2 (i^{1} i) \sqrt{2} \sqrt{2}$

Step 4.2

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

$2 (i^{1} i^{1}) \sqrt{2} \sqrt{2}$

Step 4.3

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

$2 i^{1 + 1} \sqrt{2} \sqrt{2}$

Step 4.4

Add $1$ and $1$ .

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

Step 4.5

Raise $\sqrt{2}$ to the power of $1$ .

$2 i^{2} ({\sqrt{2}}^{1} \sqrt{2})$

Step 4.6

Raise $\sqrt{2}$ to the power of $1$ .

$2 i^{2} ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 4.7

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

$2 i^{2} {\sqrt{2}}^{1 + 1}$

Step 4.8

Add $1$ and $1$ .

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

Step 5

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

$2 \cdot - 1 {\sqrt{2}}^{2}$

Step 6

Multiply $2$ by $- 1$ .

$- 2 {\sqrt{2}}^{2}$

Step 7

Rewrite ${\sqrt{2}}^{2}$ as $2$ .

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Step 7.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2}$ as $2^{\frac{1}{2}}$ .

$- 2 {(2^{\frac{1}{2}})}^{2}$

Step 7.2

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

$- 2 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 7.3

Combine $\frac{1}{2}$ and $2$ .

$- 2 \cdot 2^{\frac{2}{2}}$

Step 7.4

Cancel the common factor of $2$ .

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Step 7.4.1

Cancel the common factor.

$- 2 \cdot 2^{\frac{2}{2}}$

Step 7.4.2

Rewrite the expression.

$- 2 \cdot 2^{1}$

Step 7.5

Evaluate the exponent.

$- 2 \cdot 2$

Step 8

Multiply $- 2$ by $2$ .

$- 4$