Finite Math Examples

$\sqrt{12 x^{3}} - x \sqrt{48 x}$

Step 1

Simplify each term.

Tap for more steps...

Step 1.1

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

Tap for more steps...

Step 1.1.1

Factor $4$ out of $12$ .

$\sqrt{4 (3) x^{3}} - x \sqrt{48 x}$

Step 1.1.2

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

$\sqrt{2^{2} \cdot 3 x^{3}} - x \sqrt{48 x}$

Step 1.1.3

Factor out $x^{2}$ .

$\sqrt{2^{2} \cdot 3 (x^{2} x)} - x \sqrt{48 x}$

Step 1.1.4

Move $3$ .

$\sqrt{2^{2} x^{2} \cdot 3 x} - x \sqrt{48 x}$

Step 1.1.5

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

$\sqrt{{(2 x)}^{2} \cdot 3 x} - x \sqrt{48 x}$

Step 1.1.6

Add parentheses.

$\sqrt{{(2 x)}^{2} \cdot (3 x)} - x \sqrt{48 x}$

$\sqrt{{(2 x)}^{2} \cdot (3 x)} - x \sqrt{48 x}$

Step 1.2

Pull terms out from under the radical.

$2 x \sqrt{3 x} - x \sqrt{48 x}$

Step 1.3

Rewrite $48 x$ as ${(2^{2})}^{2} \cdot (3 x)$ .

Tap for more steps...

Step 1.3.1

Factor $16$ out of $48$ .

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

Step 1.3.2

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

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

Step 1.3.3

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

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

Step 1.3.4

Add parentheses.

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

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

Step 1.4

Pull terms out from under the radical.

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

Step 1.5

Raise $2$ to the power of $2$ .

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

Step 1.6

Multiply $4$ by $- 1$ .

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

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

Step 2

Subtract $4 x \sqrt{3 x}$ from $2 x \sqrt{3 x}$ .

$- 2 x \sqrt{3 x}$

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