Algebra Examples

$\sqrt{32 x^{3}} - 7 x \sqrt{8 x}$

Step 1

Rewrite $32 x^{3}$ as ${(4 x)}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{3}} - 7 x \sqrt{8 x}$

Step 1.2

Rewrite $16$ as $4^{2}$ .

$\sqrt{4^{2} \cdot 2 x^{3}} - 7 x \sqrt{8 x}$

Step 1.3

Factor out $x^{2}$ .

$\sqrt{4^{2} \cdot 2 (x^{2} x)} - 7 x \sqrt{8 x}$

Step 1.4

Move $2$ .

$\sqrt{4^{2} x^{2} \cdot 2 x} - 7 x \sqrt{8 x}$

Step 1.5

Rewrite $4^{2} x^{2}$ as ${(4 x)}^{2}$ .

$\sqrt{{(4 x)}^{2} \cdot 2 x} - 7 x \sqrt{8 x}$

Step 1.6

Add parentheses.

$\sqrt{{(4 x)}^{2} \cdot (2 x)} - 7 x \sqrt{8 x}$

Step 2

Pull terms out from under the radical.

$| 4 x | \sqrt{2 x} - 7 x \sqrt{8 x}$

Step 3

Remove non-negative terms from the absolute value.

$4 | x | \sqrt{2 x} - 7 x \sqrt{8 x}$

Step 4

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

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Step 4.1

Factor $4$ out of $8$ .

$4 | x | \sqrt{2 x} - 7 x \sqrt{4 (2) x}$

Step 4.2

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

$4 | x | \sqrt{2 x} - 7 x \sqrt{2^{2} \cdot 2 x}$

Step 4.3

Add parentheses.

$4 | x | \sqrt{2 x} - 7 x \sqrt{2^{2} \cdot (2 x)}$

Step 5

Pull terms out from under the radical.

$4 | x | \sqrt{2 x} - 7 x (| 2 | \sqrt{2 x})$

Step 6

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

$4 | x | \sqrt{2 x} - 7 x (2 \sqrt{2 x})$

Step 7

Multiply $2$ by $- 7$ .

$4 | x | \sqrt{2 x} - 14 x \sqrt{2 x}$