Algebra Examples

$\sqrt[3]{27 x^{3}} - \sqrt{12 x^{3}}$

Step 1

Rewrite $27 x^{3}$ as ${(3 x)}^{3}$ .

$\sqrt[3]{{(3 x)}^{3}} - \sqrt{12 x^{3}}$

Step 2

Pull terms out from under the radical, assuming real numbers.

$3 x - \sqrt{12 x^{3}}$

Step 3

Rewrite $12 x^{3}$ as ${(2 x)}^{2} \cdot (3 x)$ .

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Step 3.1

Factor $4$ out of $12$ .

$3 x - \sqrt{4 (3) x^{3}}$

Step 3.2

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

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

Step 3.3

Factor out $x^{2}$ .

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

Step 3.4

Move $3$ .

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

Step 3.5

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

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

Step 3.6

Add parentheses.

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

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

Step 4

Pull terms out from under the radical.

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

Step 5

Multiply $2$ by $- 1$ .

$3 x - 2 x \sqrt{3 x}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$