Algebra Examples

$3 x \sqrt{200 x^{3}}$

Step 1

Rewrite $200 x^{3}$ as ${(10 x)}^{2} \cdot (2 x)$ .

Tap for more steps...

Step 1.1

Factor $100$ out of $200$ .

$3 x \sqrt{100 (2) x^{3}}$

Step 1.2

Rewrite $100$ as $10^{2}$ .

$3 x \sqrt{10^{2} \cdot 2 x^{3}}$

Step 1.3

Factor out $x^{2}$ .

$3 x \sqrt{10^{2} \cdot 2 (x^{2} x)}$

Step 1.4

Move $2$ .

$3 x \sqrt{10^{2} x^{2} \cdot 2 x}$

Step 1.5

Rewrite $10^{2} x^{2}$ as ${(10 x)}^{2}$ .

$3 x \sqrt{{(10 x)}^{2} \cdot 2 x}$

Step 1.6

Add parentheses.

$3 x \sqrt{{(10 x)}^{2} \cdot (2 x)}$

Step 2

Pull terms out from under the radical.

$3 x (| 10 x | \sqrt{2 x})$

Step 3

Remove non-negative terms from the absolute value.

$3 x (10 | x | \sqrt{2 x})$

Step 4

Multiply $10$ by $3$ .

$30 x (| x | \sqrt{2 x})$

Step 5

Reorder factors in $30 x (| x | \sqrt{2 x})$ .

$30 x | x | \sqrt{2 x}$