Algebra Examples

$\sqrt{8 x} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 1

Rewrite $8 x$ as $2^{2} \cdot (2 x)$ .

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Step 1.1

Factor $4$ out of $8$ .

$\sqrt{4 (2) x} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 1.2

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

$\sqrt{2^{2} \cdot 2 x} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 1.3

Add parentheses.

$\sqrt{2^{2} \cdot (2 x)} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 2

Pull terms out from under the radical.

$| 2 | \sqrt{2 x} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 3

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

$2 \sqrt{2 x} \cdot \sqrt{4 x} \cdot \sqrt{3 x}$

Step 4

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

$2 \sqrt{2 x} \cdot \sqrt{2^{2} x} \cdot \sqrt{3 x}$

Step 5

Pull terms out from under the radical.

$2 \sqrt{2 x} \cdot (| 2 | \sqrt{x}) \cdot \sqrt{3 x}$

Step 6

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

$2 \sqrt{2 x} \cdot (2 \sqrt{x}) \cdot \sqrt{3 x}$

Step 7

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

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Step 7.1

Multiply $2$ by $2$ .

$4 \sqrt{2 x} \sqrt{x} \cdot \sqrt{3 x}$

Step 7.2

Combine using the product rule for radicals.

$4 \sqrt{x (2 x)} \cdot \sqrt{3 x}$

Step 7.3

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

$4 \sqrt{2 (x^{1} x)} \cdot \sqrt{3 x}$

Step 7.4

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

$4 \sqrt{2 (x^{1} x^{1})} \cdot \sqrt{3 x}$

Step 7.5

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

$4 \sqrt{2 x^{1 + 1}} \cdot \sqrt{3 x}$

Step 7.6

Add $1$ and $1$ .

$4 \sqrt{2 x^{2}} \cdot \sqrt{3 x}$

Step 8

Reorder $2$ and $x^{2}$ .

$4 \sqrt{x^{2} \cdot 2} \cdot \sqrt{3 x}$

Step 9

Pull terms out from under the radical.

$4 (| x | \sqrt{2}) \cdot \sqrt{3 x}$

Step 10

Multiply $4 | x | \sqrt{2} \sqrt{3 x}$ .

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Step 10.1

Combine using the product rule for radicals.

$4 | x | \sqrt{3 x \cdot 2}$

Step 10.2

Multiply $2$ by $3$ .

$4 | x | \sqrt{6 x}$