Algebra Examples

$y \sqrt{2 x} - \sqrt{8 x^{3}} + 3 \sqrt{18 x}$

Step 1

Rewrite $8 x^{3}$ as ${(2 x)}^{2} \cdot (2 x)$ .

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Step 1.1

Factor $4$ out of $8$ .

$y \sqrt{2 x} - \sqrt{4 (2) x^{3}} + 3 \sqrt{18 x}$

Step 1.2

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

$y \sqrt{2 x} - \sqrt{2^{2} \cdot 2 x^{3}} + 3 \sqrt{18 x}$

Step 1.3

Factor out $x^{2}$ .

$y \sqrt{2 x} - \sqrt{2^{2} \cdot 2 (x^{2} x)} + 3 \sqrt{18 x}$

Step 1.4

Move $2$ .

$y \sqrt{2 x} - \sqrt{2^{2} x^{2} \cdot 2 x} + 3 \sqrt{18 x}$

Step 1.5

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

$y \sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot 2 x} + 3 \sqrt{18 x}$

Step 1.6

Add parentheses.

$y \sqrt{2 x} - \sqrt{{(2 x)}^{2} \cdot (2 x)} + 3 \sqrt{18 x}$

Step 2

Pull terms out from under the radical.

$y \sqrt{2 x} - (2 x \sqrt{2 x}) + 3 \sqrt{18 x}$

Step 3

Multiply $2$ by $- 1$ .

$y \sqrt{2 x} - 2 (x \sqrt{2 x}) + 3 \sqrt{18 x}$

Step 4

Rewrite $18 x$ as $3^{2} \cdot (2 x)$ .

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Step 4.1

Factor $9$ out of $18$ .

$y \sqrt{2 x} - 2 x \sqrt{2 x} + 3 \sqrt{9 (2) x}$

Step 4.2

Rewrite $9$ as $3^{2}$ .

$y \sqrt{2 x} - 2 x \sqrt{2 x} + 3 \sqrt{3^{2} \cdot 2 x}$

Step 4.3

Add parentheses.

$y \sqrt{2 x} - 2 x \sqrt{2 x} + 3 \sqrt{3^{2} \cdot (2 x)}$

Step 5

Pull terms out from under the radical.

$y \sqrt{2 x} - 2 x \sqrt{2 x} + 3 (3 \sqrt{2 x})$

Step 6

Multiply $3$ by $3$ .

$y \sqrt{2 x} - 2 x \sqrt{2 x} + 9 \sqrt{2 x}$