Algebra Examples

$4 \sqrt{8} \cdot \sqrt{2}$

Step 1

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

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Step 1.1

Factor $4$ out of $8$ .

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

Step 1.2

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

$4 \sqrt{2^{2} \cdot 2} \cdot \sqrt{2}$

Step 2

Pull terms out from under the radical.

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

Step 3

The absolute value is the distance between a number and zero. The distance between $0$ and $2$ is $2$ .

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

Step 4

Multiply $2$ by $4$ .

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

Step 5

Multiply $8 \sqrt{2} \sqrt{2}$ .

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Step 5.1

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

$8 ({\sqrt{2}}^{1} \sqrt{2})$

Step 5.2

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

$8 ({\sqrt{2}}^{1} {\sqrt{2}}^{1})$

Step 5.3

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

$8 {\sqrt{2}}^{1 + 1}$

Step 5.4

Add $1$ and $1$ .

$8 {\sqrt{2}}^{2}$

Step 6

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

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Step 6.1

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

$8 {(2^{\frac{1}{2}})}^{2}$

Step 6.2

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

$8 \cdot 2^{\frac{1}{2} \cdot 2}$

Step 6.3

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

$8 \cdot 2^{\frac{2}{2}}$

Step 6.4

Cancel the common factor of $2$ .

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Step 6.4.1

Cancel the common factor.

$8 \cdot 2^{\frac{2}{2}}$

Step 6.4.2

Rewrite the expression.

$8 \cdot 2^{1}$

Step 6.5

Evaluate the exponent.

$8 \cdot 2$

Step 7

Multiply $8$ by $2$ .

$16$