Algebra Examples

$\sqrt{32 x^{3}} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1

Simplify each term.

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Step 1.1

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

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Step 1.1.1

Factor $16$ out of $32$ .

$\sqrt{16 (2) x^{3}} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.1.2

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

$\sqrt{4^{2} \cdot 2 x^{3}} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.1.3

Factor out $x^{2}$ .

$\sqrt{4^{2} \cdot 2 (x^{2} x)} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.1.4

Move $2$ .

$\sqrt{4^{2} x^{2} \cdot 2 x} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.1.5

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

$\sqrt{{(4 x)}^{2} \cdot 2 x} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.1.6

Add parentheses.

$\sqrt{{(4 x)}^{2} \cdot (2 x)} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.2

Pull terms out from under the radical.

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 \sqrt{2 x^{3}} + 4 \sqrt{24 x}$

Step 1.3

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

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Step 1.3.1

Factor out $x^{2}$ .

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 \sqrt{2 (x^{2} x)} + 4 \sqrt{24 x}$

Step 1.3.2

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

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 \sqrt{x^{2} \cdot 2 x} + 4 \sqrt{24 x}$

Step 1.3.3

Add parentheses.

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 \sqrt{x^{2} \cdot (2 x)} + 4 \sqrt{24 x}$

Step 1.4

Pull terms out from under the radical.

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 (x \sqrt{2 x}) + 4 \sqrt{24 x}$

Step 1.5

Rewrite $24 x$ as $2^{2} \cdot (6 x)$ .

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Step 1.5.1

Factor $4$ out of $24$ .

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 x \sqrt{2 x} + 4 \sqrt{4 (6) x}$

Step 1.5.2

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

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 x \sqrt{2 x} + 4 \sqrt{2^{2} \cdot 6 x}$

Step 1.5.3

Add parentheses.

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 x \sqrt{2 x} + 4 \sqrt{2^{2} \cdot (6 x)}$

Step 1.6

Pull terms out from under the radical.

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 x \sqrt{2 x} + 4 (2 \sqrt{6 x})$

Step 1.7

Multiply $2$ by $4$ .

$4 x \sqrt{2 x} + 2 \sqrt{6 x} - 8 x \sqrt{2 x} + 8 \sqrt{6 x}$

Step 2

Simplify by adding terms.

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Step 2.1

Subtract $8 x \sqrt{2 x}$ from $4 x \sqrt{2 x}$ .

$- 4 x \sqrt{2 x} + 2 \sqrt{6 x} + 8 \sqrt{6 x}$

Step 2.2

Add $2 \sqrt{6 x}$ and $8 \sqrt{6 x}$ .

$- 4 x \sqrt{2 x} + 10 \sqrt{6 x}$